Science
San Francisco State Electric Field Due to A Dipole Questions

San Francisco State University

Question Description

I don’t know how to handle this Physics question and need guidance.

Question #1: Electric field due to a dipole (30 points total)

An electric dipole consists of a pair of point charges with equal magnitude and opposite sign, +Q and –Q, and separated by a distance 2a, as shown.

Part A (15 points): Show that at all points on the x-axis for which , .

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Question #1: Electric field due to a dipole (30 points total) An electric dipole consists of a pair of point charges with equal magnitude and opposite sign, +Q and –Q, and separated by a distance 2a, as shown. Part A (15 points): Show that at all points on the x-axis for 𝑄𝑎 which |𝑥| ≫ 𝑎, 𝐸 ≈ 2𝜋𝜀 𝑥 3 . 0 𝑄𝑎 Part B (15 points): Show that at all points on the y-axis for which |𝑦| ≫ 𝑎, 𝐸 ≈ 𝜋𝜀 0𝑦 3 . Question #2: Electric Potential due to a dipole (30 points total) Let’s consider the same configuration as Question #1. Part A (10 points): Calculate the electric potential at any point on the x-axis. Part B (10 points): Calculate the electric potential at any point on the y-axis. Part C (10 points): Use your result in Question #2, Part B, to calculate the electric potential on the y-axis, when |𝑥| ≫ 𝑎. Use this result to confirm the answer to Question #1, Part B. Question #3: Torque on an electric dipole (20 points total) The dipole is placed in an electric field, as shown. Part A (5 points): Draw the electric forces acting on each of the charges on the figure. The net force on the electric dipole is zero, but there is a torque that tends to rotate the dipole clockwise. Part B (15 points): We define the electric dipole moment 𝑝⃗. It has a magnitude 𝑝 = 2𝑞𝑎 and its direction is along the dipole axis from the negative charge to the positive charge. Show that the net torque with respect to the center of the dipole is 𝜏⃗ = 𝑝⃗ × 𝐸⃗⃗ . Note: One method for increasing capacitance is to insert a dielectric between the conductors that reduces the voltage because of its effect on the electric field. When the molecules of a dielectric are placed in the electric field 𝐸⃗⃗ , their negatively charged electrons separate slightly from their positively charged cores, and dielectric polarization occurs. The molecules acquire an electric dipole moment. We define the polarization vector 𝑃⃗⃗ = 𝑁𝑝⃗, where N is the number of dipoles per unit volume in the material. This polarization is proportional to 𝐸⃗⃗ . Question #4: RC circuits (20 points total) Consider the RC circuits shown below. Find the magnitude and direction for the currents at the instant the switch S is closed. ...
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Final Answer

Question 4 is on the last pages here

Question #1: Electric field due to a dipole (30 points total)
An electric dipole consists of a pair of point charges with equal
magnitude and opposite sign, +Q and –Q, and separated by a
distance 2a, as shown.
Part A (15 points): Show that at all points on the x-axis for
𝑄𝑎
which |𝑥| ≫ 𝑎, 𝐸 ≈ 2𝜋𝜀 𝑥 3 .
0

𝑄𝑎

Part B (15 points): Show that at all points on the y-axis for which |𝑦| ≫ 𝑎, 𝐸 ≈ 𝜋𝜀

0𝑦

3

.

Question #2: Electric Potential due to a dipole (30 points total)
Let’s consider the ...

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