Two small spheres spaced 20.0 cm apart have equal charge. How many excess electrons
must be present on each sphere if the magnitude of the force of repulsion between
them is 4.57 10 21 N?
Three point charges are arranged on a line. Charge q 3 = +5.00 nC and is at the origin.
Charge q 2 = -3.00 nC and is at x = +4.00 cm Charge is q 1 at x = +2.00 cm. What is (magnitude
and sign) if the net force on q 3 is zero?
A charged cork ball of mass 2g is suspended on a light string in the presence of a uniform
electric field. When the field E = (3i + 4j) 105N/C, the ball is in equilibrium at = 30o. Find
the charge on the ball
g = 9.8 m/s2
A semicircular ring of radius 2mm is uniformly charged. The top half of the semicircular ring
has a total charge of –7.50 μC, whereas the bottom half has a total charge of +7.50 μC. Find,
(a) The charge per unit length on the top half and the bottom half.
(b) The magnitude and direction of the resultant electric field at O, the center of the
Four identical point charges (q = +10.0 μC) are located on the corners of a rectangle. The
dimensions of the rectangle are L = 60.0 cm and W = 15.0 cm.
(a) Calculate the magnitude and direction of the resultant electric field at the location of the
charge at the lower left corner by the other three charges.
(b) What is the magnitude and direction of the force exerted on this charge?
Three point charges are located at the corners of an equilateral triangle as shown in the Figure
(a) Calculate the resultant electric field at the location of the 7.00-μC charge.
(b) Calculate the resultant electric force on the 7.00-μC charge.
(c) ( Sheet #3)How much energy is necessary assemble these three charges at their current
Two small plastic spheres are given positive electrical charges. When they are 15.0
cm apart, the repulsive force between them has magnitude 0.220 N. What is the
charge on each sphere a) if the two charges are equal? b) if one sphere has four
times the charge of the other?
How far does the electron of a hydrogen atom have to be removed from the
nucleus for the force of attraction equal the weight of the electron at the surface of
A negative charge -0.550 μC exerts an upward 0.200-N force on an unknown charge
0.300 m directly below it. a) What is the unknown charge (magnitude and sign)? b)
What are the magnitudes and direction of the force that the unknown charge exerts on
the -0.550 μC charge?
Two point charges are placed on the x-axis as follows: charge
q = +5.00 nC is at x = _0.300 m. What are the magnitude and direction of the total force
exerted by these two charges on a negative point charge
q3 = -6.00 nC that is placed at the origin?
a) What must the charge (sign and magnitude) of a 1.45-g particle be for it to
remain stationary when placed in a downward directed electric field of magnitude
650 N/C? b) What is the magnitude of an electric filed in which the electric force
on proton is equal in magnitude to weight?
A uniform electric field exists in the region between two oppositely charged plane
parallel plates. A proton is released from rest at the surface of the positively
charged plate and strikes the surface of the opposite plate, 1.60
cm distant from the first, in a time interval of 1.50 × 10-6 s. a) Find the magnitude
of the electric field. b) Find the speed of proton when it strikes the negatively
Avery long, straight wire has charge per unit length 1.50 × 10-10 C/m. At what
distance from the wire is the electric field magnitude equal to 2.50 N/C?
Near the earth’s surface, the electric field in the open air has magnitude 150 N/C
and is directed down toward the ground. If this is regarded as being due to a large
sheet of charge lying on the earth’s surface, calculate the charge a in the per unit
area in the sheet. What is the sign of the charge?
point charged q1 = -4.5 nC and q2 = +4.5 nC are separated by 3.1 mm, forming an
electric dipole. a) Find the electric dipole moment (magnitude and direction). b)
The charges are in the uniform electric whose direction makes an angle of 36.9ο
with the line connecting the charges. What is the magnitude of this field if the
torque exerted on the dipole has magnitude 7.2 × 10-9 N.m?
A hollow non-conducting spherical shell of inner radius R1 and outer radius R2 carries a total
charge of Q distributed uniformly throughout its volume. Determine the electric flux through a
spherical surface of radius r (R1b).
c- Repeat (a), and (b) if a net charge of -2.5 C is placed on the shell.
A solid copper sphere of radius 15.0 cm carries a charge of 40.0 nC. Find the electric
field (a) 12.0 cm, (b) 17.0 cm, and (c) 75.0 cm from the center of the sphere. (d) What If?
How would your answers change if the sphere were hollow?
A solid plastic sphere of radius 10.0 cm has charge with uniform density throughout its
volume. The electric field 5.00 cm from the center is 86.0 kN/C radially inward. Find
a) The total charge on the sphere
b) the magnitude of the electric field 15.0 cm from the center.
A conducting spherical shell of inner radius a and outer radius b carries a net charge Q.
A point charge q is placed at the center of this shell. Determine
(a)the electric fields at each of the following regions r b
(b) the surface charge density on the inner surface of the shell and
(c) the surface charge density on the outer surface of the shell.
A point charge q is located at the center of a uniform ring having linear charge density λ
and radius a, as shown in the Figure Determine the total electric flux through a sphere
centered at the point charge and having radius R, where R < a.
An insulating sphere is 8.00 cm in diameter and carries a 5.70-μC charge uniformly
distributed throughout its interior volume. Calculate the charge enclosed by a
concentric spherical surface with radius (a) r = 2.00 cm and (b) r = 6.00 cm
It is found experimentally that the electric field in a certain region of the earth's atmosphere is
directed vertically downward. At an altitude of 300m the filed is 60N/C and at an altitude of
200m it is 100N/C.
(a) The net flux through a cube with each edge of length 100m located between the altitudes
of 200m and 300m.
(b) The net amount of charge contained in a cube 100m on edge located at an altitude
between 200m and 300m.
[Hint: Draw a cube with each edge length 100m located between the altitudes of 200m and
Two parallel non-conducting rings arranged with their central axes along a common line. Ring 1
has uniform charged –q and radius R: ring 2 has uniform charge q and the same radius R. The
rings are separated by a distance 2R.
a) With V= 0 at infinity, derive an expression for the electric potential V at point P on the
common line, at a distance x from the origin O.
b) Derive an expression for the net electric filed E (magnitude and direction) at point P?
Three point charges q1= 5 μC, q2 = 4 μC , and q3 = 1 μC are shown in the figure.
a. With V= 0 at infinity, find the electric potential V at point P located on the x axis at x = 2 m.
b. A proton is placed at point P (x = 2 m), the speed of the proton when it is very far from the three
An electron moving parallel to the x axis has an initial speed of 3.70 × 106 m/s at the origin. Its
speed is reduced to 1.40 × 105 m/s at the point x = 2.00 cm. Calculate,
(a) the potential difference between the origin and that point.
(b) if the electric in the region between the origin and the x = 2.00 cm is constant, what the
magnitude and the direction of this electric field.
(c) Which point is at the higher potential?
A thin ring of radius R carries a positive charge Q spread uniformly over its circumference.
(a) Starting from the definition of the potential of a point charge, derive an expression for the
potential created by the ring at a distance x from its center along the axis of the ring.
(b) If an electron is released from rest at x R 3 , how fast will it be moving when it reaches the
Four point charges, q 2 nC each, are fixed in position at the corners of a square 3 m on a side.
Calculate the electrostatic potential energy (in electron volts) of an electron placed at the center
of the square. nC 10 -9 C, 1 eV 1.6 10 19 J .
A proton (mass = 1.67 10–27 kg, charge = 1.60 10–19 C) moves from point A to point B under the
influence of an electrostatic force only. At point A the proton moves with a speed of 60 km/s. At
point B the speed of the proton is 80 km/s. Determine the potential difference V B V A . [Hint: use
conservation of energy.]
Charge Q is distributed uniformly over a non-conducting ring of radius R .
a) Derive an expression for the potential V (z ) at a point on the axis of the ring a
distance z from its center.
b) Use the expression derived above to find the electric field strength E z at the same
point. k e 9 10 9 Nm2 /C 2 , e 1.6 10 19 C .
Evaluate V and E z for Q due to a million electrons, R 3 cm and z 4 cm.
The figure shows an annulus of inner radius a = 2.0 cm and an outer radius b = 5.0 cm. The
annulus has a uniform charge surface density = 1.5x106C/m2.
a) With V= 0 at infinity calculate the electric potential V at point C the center of
b) What is the magnitude of the electric field at point C?
c) What is the total charge q on the surface?
Two charges q1 = 5 C and q2 = +2C are located at the opposite corners of a rectangle.
With V= 0 at infinity, and A and B are the at opposite corners of the rectangle, as shown,
a) what is the electric potential at point A?
b) What is the electric potential at point B?
c) How much work is required to move a third charge q3 = +3C from point B to
point A along the diagonal of the rectangle?
1. A charged particle (q= - 8.0 mC), which moves in a region where the only force acting
on the particle is an electric force, is released from rest at point A. At point B the kinetic
energy of the particle is equal to 4.8 J. What is the electric potential difference (VBVA)?
2. If a = 30 cm, b = 20 cm, q = + 2.0 nC and Q = - 3.0 nC in the figure, what is the
potential difference (VA-VB)?
A uniform electric field of magnitude 325 V/m is directed in the negative y direction in
the Figure. The coordinates of point A are
(–0.200, –0.300) m, and those of point B
are (0.400, 0.500) m. Calculate the potential difference VB – VA, using the shown path.
Given two 2.00-μC charges, as shown in the Figure, What is the electrical potential at
the origin due to the two 2.00-μC charges?
Four capacitors are connected as shown in the Figure below.
(a) Find the equivalent capacitance of the network.
(b) Calculate the charge on each capacitor and the voltage across each capacitor if a DC battery
of 15.0 V is applied at point a.
(c) Calculate the energy stored in each capacitor.
Two capacitors C1 and C2 (where C1 > C2) are charged to the same potential difference V. The
charged capacitors are removed from the battery and their plates are connected with opposite
polarity, i.e., the positive plate of C1 is connected to the negative plate of C2 and vice versa.
(a) The voltage, charge and the energy in each capacitor before they are connected to each
(b) The voltage, charge and the energy in each capacitor after they are connected to each
Given, C1 = 30µF, C2 = 20 µF, and V = 12Volts
In the circuit below, C1 = 15 µF, C2 = 10 µF, C3 = 20 µF, and V0 = 18 V. Determine
a) The equivalent capacitance.
b) The charge stored on C2.
c) The energy stored in C3.
A parallel-plate capacitor has plates of area A = 0.12m2 each and a separation d = 1.2 cm. A battery
charges the plates to a potential difference of 120 V and then disconnected. A dielectric slab of
thickness of 4 mm and dielectric constant K = 4 is then placed symmetrically between the plates.
a) What is the capacitance C of the capacitor before and after the slab is inserted?
b) What is the charge q on the capacitor before and after the slab is inserted?
c) With the slab in place the plates, what is the potential difference across the plates?
A parallel plate capacitor of capacitance Co has plates area A with separation d between them. When it
is connected to a battery of voltage Vo it has charge of magnitude Qo on its plates. The plates are pulled
apart to a separation 2d while the capacitor remains connected to the battery. After the plates are 2d
apart, find the
a. a. magnitude of the charge on the plates and
b. the potential difference between them.
A parallel plate capacitor of capacitance Co has plates area A with separation d between them. When it
is connected to a battery of voltage Vo it has charge of magnitude Qo on its plates. While it is connected
to the battery the space between the plates is filled with a material of dielectric constant 3. After the
dielectric is added, find
c. the magnitude of the charge on the plates and
d. the potential difference between them.
Consider the circuit shown in the Figure, where C1 = 6.00 μF, C2 = 3.00 μF, and ΔV = 20.0 V.
Capacitor C1 is first charged by the closing of switch S1. Switch S1 is then opened, and the
charged capacitor is connected to the uncharged capacitor by the closing of S2. Calculate the
initial charge acquired by C1 and the final charge on each capacitor.
Purchase answer to see full