PHYS 260 Skyline College Electrical Energy Questions Sets

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ruoyijin@my.smccd.edu (sign out) Home My Assignments Communication Grades Calendar My eBooks PHYS 260, section All, Spring 2020 INSTRUCTOR Emilie Hein HW 12 - PHYS 260 - (Homework) Skyline College, CA Current Score QUESTION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 POINTS 0/1 –/1 1/2 2/2 2/2 2/2 –/4 4/4 –/4 2/4 –/1 1/2 4/4 –/4 –/4 –/1 2/3 1/2 1/2 TOTAL SCORE 22/49 44.9% Due Date SUN, MAY 17, 2020 11:00 PM PDT Assignment Submission & Scoring Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. 1. [0/1 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 29.1.WA.001. MY NOTES A wire carrying a current of 2.60 A has a straight segment of 2.45 m. Determine the magnitude of the magnetic field due to this segment of wire at a point P which is at the midpoint of the straight segment of wire and a distance of 0.270 m perpendicular to the wire. 1.93e-6 Can you find an expression for the result of applying the Biot-Savart law to a finite length of a straight segment of a current carrying wire? T Additional Materials eBook 2. [–/1 Points] DETAILS OSUNIPHYS1 29.1.WA.002. MY NOTES A wire carrying a current of 3.00 A has a straight segment of 2.15 m. Determine the magnitude of the magnetic field due to this segment of wire at a point P which is at the end of the straight segment of wire and a distance of 2.52 m perpendicular to the wire. T Additional Materials eBook 3. [1/2 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 29.1.WA.003. MY NOTES An infinitely long wire carrying a current of 2.65 A is bent at a right angle as shown in the figure. Determine the magnitude and direction of the magnetic field at the point P a distance a = 21.3 cm from each leg of the right angle bend. magnitude direction −k Additional Materials eBook T 4. [2/2 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 29.1.P.019. MY NOTES The accompanying figure shows a current loop consisting of two concentric circular arcs and two perpendicular radial lines. Determine the magnetic field at point P. (Use the following as necessary: a, b, I and μ0.) magnitude B = direction † Additional Materials eBook μ0I(b−a)8ab out of the page 5. [2/2 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 29.1.P.021. MY NOTES Two long wires, one of which has a semicircular bend of radius R, are positioned as shown in the accompanying figure. If both wires carry a current I, how far apart must their parallel sections be so that the net magnetic field at P is zero? (Use the following as necessary: R.) a= 2Rπ Does the current in the straight wire flow up or down? The current in the wire to the right must flow up the page. The current in the wire to the right must flow down the page. † Additional Materials eBook 6. [2/2 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 29.1.WA.005. MY NOTES An infinitely long wire carrying a current of 4.40 A is bent at a right angle in such a manner that the bend is the arc of a circle with a radius of r = 12.5 cm as shown in the figure. Determine the magnitude of the magnetic field at the point P which is at the center of the arc. 1.25e-5 T Determine the direction of the magnetic field at the point P which is at the center of the arc. î −î ĵ −ĵ − Additional Materials eBook 7. [–/4 Points] DETAILS OSUNIPHYS1 29.1.WA.007. MY NOTES A conducting loop resting in the xy plane is in the shape of a rectangle with a short side of length L and a long side of length 2L, where L = 21.9 cm. The current in the loop is 2.67 A and travels in the counter-clockwise direction when viewed from the +z axis. (a) Determine the magnitude and direction of the magnetic field at the center of the loop. magnitude direction T ---Select--- (b) If the conductor is now reshaped to form a circle (also in the xy plane) in which the current travels in the counterclockwise direction, when viewed from the +z axis, determine the magnitude and direction of the magnetic field at the center of the loop. magnitude direction Additional Materials eBook T ---Select--- 8. [4/4 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 29.2.P.027. MY NOTES The accompanying figure shows two long, straight, horizontal wires that are parallel and a distance 2a apart. If both wires carry current I in the same direction, what is the magnetic field at the following locations? (Use the following as necessary: a, I and μ0.) (a) P1 magnitude B = 0 The magnitude is zero. direction (b) P2 magnitude direction † Additional Materials eBook B = 3μ0I8πa into the page 9. [–/4 Points] DETAILS OSUNIPHYS1 29.2.WA.010. MY NOTES As shown in the figure below, two long parallel wires (1 and 2) carry currents of I1 = 3.30 A and I2 = 4.50 A in the direction indicated. (a) Determine the magnitude and direction of the magnetic field at a point midway between the wires (d = 10.0 cm). magnitude µT direction ° counterclockwise from the +x axis (b) Determine the magnitude and direction of the magnetic field at point P, located d = 10.0 cm above wire 1. magnitude µT direction ° counterclockwise from the +x axis Additional Materials eBook 10. [2/4 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 29.2.WA.013.TUTORIAL. MY NOTES As shown in the figure, two long, straight current-carrying wires (1 and 2) are attached at right angles to a board by wire brackets. The current in wire 1 is 19.1 A in the negative y direction and the current in wire 2 is 5.00 A in the positive x direction. The points A and B are a distance r = 0.200 m from both wires. (a) How does the magnitude of the net magnetic field at point A compare to the magnitude of the net magnetic field at point B? BA > BB BA = BB BA < BB (b) Determine the magnitude of the net magnetic field at points A and B. point A T point B T (c) If the brackets holding wire 2 are removed, what will happen to wire 2? It will rotate clockwise. It will rotate counterclockwise. Nothing will happen. Additional Materials eBook Tutorial 11. [–/1 Points] DETAILS OSUNIPHYS1 29.4.P.035. MY NOTES When the current through a circular loop is 7.5 A, the magnetic field at its center is 3.1 ✕ 10−4 T. What is the radius (in m) of the loop? m † Additional Materials eBook 12. [1/2 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 29.4.WA.027.TUTORIAL. MY NOTES The figure below shows a long straight wire just touching a circular loop carrying a current I1 = 2.58 A in the counterclockwise direction. Both lie in the same plane. (a) What direction must the current I2 in the straight wire have in order to create a magnetic field at the center of the loop in the direction opposite to that created by the loop? from right to left from left to right (b) What current must the long straight wire carry in order to have zero net magnetic field strength at the center of the loop? A Additional Materials eBook Tutorial 13. [4/4 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 29.5.P.041. A current I flows around the rectangular loop shown in the accompanying figure. Evaluate any variable or symbol stated above along with the following as necessary: μ0.) path A B · dl = μ0·I path B B · dl = 0 path C B · dl = μ0·I path D B · dl = 0 † Additional Materials eBook MY NOTES B · d l for the following paths. (Use 14. [–/4 Points] DETAILS OSUNIPHYS1 29.5.WA.031. MY NOTES Consider the seven current-carrying wires and the four closed paths shown in the figure. For each of these paths (C1, C2, C3, and C4) determine the following in terms of μ0. Use standard sign convention for the currents; minus is down into the page and positive is up out of the page. (Assume I1 = 3.00 A, I2 = 6.00 A, I3 = 4.00 A, I4 = 6.00 A, I5 = 5.00 A, I6 = 6.00 A, and I7 = 7.00 A.) B · ds = A μ0 B · ds = A μ0 B · ds = A μ0 B · ds = A μ0 (a) C1 (b) C2 (c) C3 (d) C4 Additional Materials eBook 15. [–/4 Points] DETAILS OSUNIPHYS1 29.5.P.043. MY NOTES The coil whose lengthwise cross section is shown in the accompanying figure carries a current I and has N evenly spaced turns distributed along the length l. Evaluate B · d l for the paths indicated. (Use any variable or symbol stated above along with the following as necessary: μ0.) path A B · dl = path B B · dl = path C B · dl = path D B · dl = † Additional Materials eBook 16. [–/1 Points] DETAILS OSUNIPHYS1 29.6.P.055. MY NOTES A solenoid with 33 turns per centimeter carries a current I. An electron moves within the solenoid in a circle that has a radius of 3.0 cm and is perpendicular to the axis of the solenoid. If the speed of the electron is 3.6 ✕ 105 m/s, what is I (in A)? A † Additional Materials eBook [2/3 Points] 17. DETAILS PREVIOUS ANSWERS OSUNIPHYS1 29.3.P.030. MY NOTES Two long, straight wires are parallel and 21 cm apart. (a) If each wire carries a current of 63 A in the same direction, what is the magnitude of the magnetic force per meter (in N/m) exerted on each wire? N/m (b) Does the force pull the wires together or push them apart? The wires are pulled together. The wires are pushed apart. The magnetic force per meter is zero. (c) What happens if the currents flow in opposite directions? The wires are pulled together. The wires are pushed apart. The magnetic force per meter is zero. † Additional Materials eBook 18. [1/2 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 29.3.WA.019. MY NOTES Two power lines run parallel for a distance of 291 m and are separated by a distance of 40.0 cm. If the current in each of the two lines is 100 A and if they run in opposite directions, determine the magnitude and direction of the force each wire exerts on the other. magnitude direction away from each other Additional Materials eBook N 19. [1/2 Points] DETAILS PREVIOUS ANSWERS OSUNIPHYS1 29.3.WA.021. MY NOTES The figure below shows a long straight wire near a rectangular current loop. The current in the wire is I1 = 18.0 A and the current in the loop is I2 = 30.0 A. The dimensions of the loop are L = 36.0 cm,w = 12.0 cm, and the distance from the loop to the wire is r = 9.00 cm. Determine the magnitude and direction of the total force on the loop. magnitude direction N away from the wire Additional Materials eBook Submit Assignment Home Copyright Save Assignment Progress My Assignments 2020 Cengage Learning, Inc. All Rights Reserved ruoyijin@my.smccd.edu (sign out) Home My Assignments Grades Communication Calendar My eBooks PHYS 260, section All, Spring 2020 INSTRUCTOR Emilie Hein HW 13 - PHYS 260 - (Homework) Skyline College, CA Current Score QUESTION 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 POINTS –/1 –/3 –/2 –/2 –/1 –/3 –/1 –/1 –/1 –/2 –/1 –/2 –/4 –/6 –/4 TOTAL SCORE –/34 0.0% Due Date SUN, MAY 17, 2020 11:00 PM PDT Assignment Submission & Scoring Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. 1. [–/1 Points] DETAILS OSUNIPHYS1 29.6.P.055. MY NOTES A solenoid with 32 turns per centimeter carries a current I. An electron moves within the solenoid in a circle that has a radius of 2.7 cm and is perpendicular to the axis of the solenoid. If the speed of the electron is 4.4 ✕ 105 m/s, what is I (in A)? A † Additional Materials eBook 2. [–/3 Points] DETAILS OSUNIPHYS1 29.3.P.030. MY NOTES Two long, straight wires are parallel and 49 cm apart. (a) If each wire carries a current of 53 A in the same direction, what is the magnitude of the magnetic force per meter (in N/m) exerted on each wire? N/m (b) Does the force pull the wires together or push them apart? The wires are pulled together. The wires are pushed apart. The magnetic force per meter is zero. (c) What happens if the currents flow in opposite directions? The wires are pulled together. The wires are pushed apart. The magnetic force per meter is zero. † Additional Materials eBook 3. [–/2 Points] DETAILS OSUNIPHYS1 29.3.WA.019. MY NOTES Two power lines run parallel for a distance of 283 m and are separated by a distance of 40.0 cm. If the current in each of the two lines is 130 A and if they run in opposite directions, determine the magnitude and direction of the force each wire exerts on the other. magnitude direction ---Select--- Additional Materials eBook N 4. [–/2 Points] DETAILS OSUNIPHYS1 29.3.WA.021. MY NOTES The figure below shows a long straight wire near a rectangular current loop. The current in the wire is I1 = 17.0 A and the current in the loop is I2 = 30.0 A. The dimensions of the loop are L = 30.0 cm, w = 10.0 cm, and the distance from the loop to the wire is r = 6.00 cm. Determine the magnitude and direction of the total force on the loop. magnitude direction N ---Select--- Additional Materials eBook 5. [–/1 Points] DETAILS OSUNIPHYS1 29.3.WA.024. MY NOTES Two long parallel wires in the xy plane repel each other with a force per unit length of 290 µN/m. One wire runs along the x axis and carries a current of 15.0 A in the positive x direction. The other wire runs along the line y = d, where d = 0.540 m. Determine the y value for the location of a line in the xy plane along which the total magnetic field is zero. (Include the sign of the value in your answer.) m Additional Materials eBook 6. [–/3 Points] DETAILS OSUNIPHYS1 29.3.WA.025. MY NOTES Three long wires are all parallel to each other and are all in the xy plane. Wire 1 runs along the y axis and carries a current of 1.88 A in the +y direction. Wire 2 runs along the x = 25.0 cm line and carries a current of 4.02 A in the −y direction. (a) Determine the location of wire 3 on the x axis so that when it carries a certain current (to be determined later) each wire experiences no net force. m (b) Determine the magnitude and direction of the current in wire 3. magnitude direction Additional Materials eBook A ---Select--- 7. [–/1 Points] DETAILS OSUNIPHYS1 30.1.P.027. MY NOTES The magnetic field through a circular loop of radius 17.1 cm varies with time as shown below. The field is perpendicular to the loop. Plot the magnitude of the induced emf in the loop as a function of time. † Additional Materials eBook 8. [–/1 Points] DETAILS OSUNIPHYS1 30.1.P.031. MY NOTES A rectangular wire loop with length a and width b lies in the xy-plane, as shown below. Within the loop there is a time-dependent magnetic field given by B(t) = C (x cos(ωt))î + (y sin(ωt)) , with B(t) in teslas. Determine the emf induced in the loop as a function of time. (Enter the magnitude. Use the following as necessary: a, b, ω, t and C.) (t) = † Additional Materials eBook 9. [–/1 Points] DETAILS OSUNIPHYS1 30.1.WA.001. MY NOTES A long straight wire carries a current of 2.50 A as shown in the figure. The distance r1 = 10.0 cm, r2 = 20.0 cm, and ℓ = 11.0 cm. Determine the magnitude of the magnetic flux through the area shown. Wb Additional Materials eBook 10. [–/2 Points] DETAILS OSUNIPHYS1 30.2.WA.020.TUTORIAL. MY NOTES A single turn coil of radius 4.50 cm is held in a vertical plane and a magnet is rapidly moved relative to the coil as shown in the diagram below. The field inside the coil changes from 0.550 T to 0.235 T in 0.120 s. If the resistance of the coil is 3.90 Ω, what are the magnitude and direction of the induced current in the coil as viewed from the side of the magnet? magnitude direction ---Select--- Additional Materials eBook Tutorial mA 11. [–/1 Points] DETAILS OSUNIPHYS1 30.2.WA.021.TUTORIAL. MY NOTES A wire of length L is wound around an iron cylinder mounted on a base. The two ends of the wire are connected to a battery via a switch that is initially open. A metal ring with a diameter larger than that of the cylinder sits on top of the coil. What happens to the metal ring when the switch is closed? The ring will move away from the coil and fly upward. The ring will move toward the coil. The ring will remain stationary. Additional Materials eBook Tutorial 12. [–/2 Points] DETAILS OSUNIPHYS1 30.2.WA.014. MY NOTES A long, straight wire carrying a current of 3.30 A moves with a constant speed v to the right. A 5-turn circular coil of diameter 1.25 cm, and resistance of 3.25 µΩ, lies stationary in the same plane as the straight wire. At some initial time, the wire is at a distance d = 13.0 cm from the center of the coil. 5.10 s later, the wire is at a distance 2d from the center of the coil. What is the magnitude and direction of the average induced current in the coil? Note that while the magnetic field varies over the diameter of the coil, it is very small and we will disregard this variation. magnitude direction ---Select--- Additional Materials eBook mA 13. [–/4 Points] DETAILS OSUNIPHYS1 30.2.WA.017. MY NOTES A coil lies on a horizontal plane and the south pole of the magnet is thrust into the coil with a quick movement in the direction shown in the diagram below. Find the direction of the induced current in the coil, when looking down on the coil from above, by answering the following questions. (a) What is the direction of the magnetic field due to the magnet in the center of the coil? +x −x +y −y +z −z (b) As the magnet is moved in the direction indicated, how will the magnetic flux in the coil change? increase decrease remain the same (c) What is the direction of the induced magnetic flux in the coil? +x −x +y −y +z −z (d) What is the direction of the induced current in the coil when viewed from above the coil? clockwise counterclockwise no current Additional Materials eBook 14. [–/6 Points] DETAILS OSUNIPHYS1 30.2.WA.016. MY NOTES A coil is placed next to a straight wire. The current in the wire is as shown in the diagram below. The coil and wire lie in the same plane with the +z axis perpendicular to the plane of the coil. (a) As the current in the wire increases, find the direction of the induced current in the coil by answering the following questions. (i) What is the direction of the magnetic field due to the current-carrying wire in the coil? +x −x +y −y +z −z (ii) As the current in the wire increases, how will the magnetic flux in the coil change? increase remain the same decrease (iii) What is the direction of the induced magnetic flux in the coil? +x −x +y −y +z −z (iv) What is the direction of the induced current in the coil? clockwise counterclockwise no current (b) Now suppose the current in the wire decreases. What is the direction of the induced current in the coil? clockwise counterclockwise no current (c) Now suppose the current in the wire suddenly changes direction. What is the direction of the induced current in the coil? clockwise counterclockwise no current Additional Materials eBook 15. [–/4 Points] DETAILS OSUNIPHYS1 30.2.WA.018. MY NOTES Two concentric coils of wire lie on a horizontal flat surface. The smaller coil is connected to a battery and a switch. The diagram shows the top view of the set up. (a) Initially the switch is open. What is the direction of the induced current in Coil 2? clockwise counterclockwise no current (b) Now the switch is closed. Immediately after the switch is closed, what is the direction of the induced current in Coil 2? clockwise counterclockwise no current (c) A long time after the switch is closed, what is the direction of the induced current in Coil 2? clockwise counterclockwise no current (d) Now the switch is opened once again. Immediately after the switch is open what is the direction of the induced current in Coil 2? clockwise counterclockwise no current Additional Materials eBook Submit Assignment Home Copyright Save Assignment Progress My Assignments 2020 Cengage Learning, Inc. All Rights Reserved ruoyijin@my.smccd.edu (sign out) Home My Assignments Communication Grades Calendar My eBooks PHYS 260, section All, Spring 2020 INSTRUCTOR Emilie Hein HW 14 - PHYS 260 - (Homework) Skyline College, CA Current Score QUESTION 1 2 3 4 5 6 7 8 9 10 POINTS –/2 –/3 –/3 –/1 –/2 –/1 –/1 –/8 –/1 –/3 TOTAL SCORE –/25 0.0% Due Date SUN, MAY 17, 2020 11:00 PM PDT Assignment Submission & Scoring Assignment Submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. 1. [–/2 Points] DETAILS OSUNIPHYS1 32.6.P.044. MY NOTES A step-up transformer is designed so that the output of its secondary winding is 2,200 V (rms) when the primary winding is connected to a 190 V (rms) line voltage. (a) If there are 200 turns in the primary winding, how many turns are there in the secondary winding? turns (b) If a resistor connected across the secondary winding draws an rms current of 0.55 A, what is the current (in A) in the primary winding? A † Additional Materials eBook 2. [–/3 Points] DETAILS OSUNIPHYS1 32.6.WA.041.TUTORIAL. MY NOTES (a) What is the voltage output of a transformer used for rechargeable flashlight batteries if its primary has 483 turns, its secondary has 8 turns, and the input voltage is 110 V? V (b) What input current is required to produce a 4.00 A output? mA (c) What is the power input? W Additional Materials eBook Tutorial 3. [–/3 Points] DETAILS OSUNIPHYS1 32.6.WA.042. MY NOTES A large power plant generates electricity at 12.0 kV. Its old transformer once converted the voltage to 403 kV. The secondary of this transformer is being replaced so that its output can be 510 kV for more efficient cross-country transmission on upgraded transmission lines. (a) What is the ratio of turns in the new secondary to turns in the old secondary? Ns, new = Ns, old (b) What is the ratio of new current output to old output (at 403 kV) for the same power? Is, new = Is, old (c) If the upgraded transmission lines have the same resistance, what is the ratio of new line power loss to old? Pnew = Pold Additional Materials eBook 4. [–/1 Points] DETAILS OSUNIPHYS1 31.4.P.055. MY NOTES How long after switch S1 is thrown does it take the current in the circuit shown to reach three-fourths its maximum value? Express your answer in terms of the time constant τ of the circuit. t= † Additional Materials eBook 5. [–/2 Points] DETAILS OSUNIPHYS1 31.4.P.057. MY NOTES The current in the RL circuit shown below reaches two-thirds its maximum value in 1.25 ms after the switch S1 is thrown. (a) Determine the time constant of the circuit (in ms). ms (b) Determine the resistance of the circuit (in Ω) if L = 200 mH. Ω † Additional Materials eBook 6. [–/1 Points] DETAILS OSUNIPHYS1 31.4.WA.016. MY NOTES The circuit below shows a simple RL circuit. Which of the graphs below correctly shows the current versus time soon after the switch is moved to position 1 as shown in the figure above? Additional Materials eBook 7. [–/1 Points] DETAILS OSUNIPHYS1 31.4.WA.017. MY NOTES The circuit below shows a simple RL circuit. Initially, the switch is in position 1. Which of the graphs below correctly shows the current versus time soon after the switch is moved to position 2 as shown in the figure above? Additional Materials eBook 8. [–/8 Points] DETAILS OSUNIPHYS1 31.4.P.059. MY NOTES = 60 V, R1 = 21 Ω, R2 = 42 Ω, R3 = 63 Ω, and L = 4.0 mH. Find the values of I1 and I2 (in A) at the following times. (Indicate the direction with the signs of your answers.) For the circuit shown below, (a) immediately after switch S is closed I1 = A I2 = A (b) a long time after S is closed (c) I1 = A I2 = A immediately after S is reopened (Assume the circuit has reached a steady state before S is reopened.) I1 = A I2 = A (d) a long time after S is reopened I1 = A I2 = A † Additional Materials eBook [–/1 Points] 9. DETAILS OSUNIPHYS1 31.4.WA.027. MY NOTES A 40.0 cm long solenoid has a diameter of 10.0 cm and 1000 loops. How much energy is stored in this inductor when 18.8 A of current flows through it? J Additional Materials eBook 10. [–/3 Points] DETAILS OSUNIPHYS1 31.4.WA.028.TUTORIAL. MY NOTES A 1.80-H inductance coil and a 11.2 Ω resistor are connected in series with a battery whose emf is 115 V and a switch. Initially, the switch is open. At t = 0, the switch is closed. (a) Determine the rate at which energy is stored in the magnetic field at t = 0.150 s. W (b) Determine the rate at which thermal energy is dissipated through the resistance at t = 0.150 s. W (c) Determine the rate at which the battery delivers energy at t = 0.150 s. W Additional Materials eBook Tutorial Submit Assignment Home Copyright Save Assignment Progress My Assignments 2020 Cengage Learning, Inc. All Rights Reserved
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Explanation & Answer:
Electrical Energy Questions Sets
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Explanation & Answer

Here's the first set of solutions. The first few items were typewritten via LaTeX so it was a bit long to type in solutions. However, the reams of paper I've ordered arrived so I continued using paper and attached pictures of the solutions for the rest of the items.

SET 1
Solutions

From these angle relationships, the integral now becomes

1. Consider the general case where a point is placed arbitrarily at any point near a finite length
of a conducting wire.

⃗ =
𝐵

𝐼𝜇0 𝑎 𝑠𝑒𝑐 2 (𝜃) 𝑐𝑜𝑠(𝜃)
𝐼𝜇0

𝑑𝜃 𝑘̂ =
∫ 𝑐𝑜𝑠(𝜃) 𝑑𝜃 𝑘̂
2
2
4𝜋
𝑎 𝑠𝑒𝑐 (𝜃)
4𝜋𝑎

We are now integrating with respect to the angles from point 𝑃. The integral therefore is
⃗ =
𝐵

⃗ =
𝐵

Utilizing the Biot – Savart Law, the magnetic field at a given point 𝑃 can be calculated using
⃗ =
𝐵

𝜇0 𝐼𝑑𝑠 × 𝑟̂ 𝐼𝜇0 ‖𝑑𝑠‖‖𝑟̂ ‖ 𝑠𝑖𝑛 𝛾
𝐼𝜇0 𝑑𝑠 𝑠𝑖𝑛(𝛾)

=

𝑘̂ =

𝑘̂
2
2
4𝜋
𝑟
4𝜋
𝑟
4𝜋
𝑟2

𝐼𝜇0 𝜃2
∫ 𝑐𝑜𝑠(𝜃) 𝑑𝜃 𝑘̂
4𝜋𝑎 −𝜃1

𝐼𝜇0
[𝑠𝑖𝑛(𝜃2 ) + 𝑠𝑖𝑛(𝜃1 )] 𝑘̂
4𝜋𝑎

For any finite length of conducting wire, we only need to know the angles −𝜃1 and 𝜃2 to
compute for the magnetic field at any point near the wire.
For this problem, we have a wire carrying a current 𝐼 = 2.60 𝐴.

since the current is constant everywhere along the wire and the magnitude of the unit
vector 𝑟̂ is simply 1.
Notice that the small elements of the wire 𝑑𝑠 contributes a magnetic field at point 𝑃 and are
governed respectively by the angles −𝜃1 and 𝜃2 . Therefore, we can express the integral in
terms of the angles −𝜃1 and 𝜃2 to compute for the total magnetic field distribution of the
finite segment of a conducting wire.
Notice that
𝑎
𝑠𝑖𝑛(𝛾) = 𝑠𝑖𝑛(𝜋 − 𝛾) = = 𝑐𝑜𝑠(𝜃)
𝑟

Since the point is on the midline of the wire, we know that the angles will be equal.
Calculating for the angle 𝜃,
𝑡𝑎𝑛(𝜃) = [

2.45
]
2(0.270)

Also notice the angle re...


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