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Chapter 4: Q17E (page 778)

Point charges q1 = +2.00 碌C and q2 = -2.00 碌C are placed at adjacent corners of a square for which the length of each side is 3.00 cm. Point a is at the center of the square, and point b is at the empty corner closest to q2. Take the electric potential to be zero at a distance far from both charges.

(a) What is the electric potential at point a due to q1 and q2?

(b) What is the electric potential at point b?

(c) A point charge q3 = -5.00 碌C moves from point a to point b. How much work is done on q3 by the electric forces exerted by q1 and q2? Is this work positive or negative?

Short Answer

Expert verified
  1. The electric potential at a point due to q1 and q2 is Zero.
  2. The electric potential at b is -175 KV.
  3. the work done in moving a charge from a to be is -0.875 Joules

Step by step solution

01

Given Data and concept

q1 = 2.0010-6 C

q2 = - 2.0010-6 C

q3 = -5.0010-6 C

The electric potential at point r due to point charge q can be written as:

V=Kqr

Here V is the potential.

02

Electric Potential due to q1 and q2

(a)

Electric Potential due both charges at a point is given by,

Va=kq1d+kq2d=kd2.00渭C-2.00渭c=0

Therefore, the electric potential at a point due to q1 and q2 is Zero.

03

Electric Potential at b

(b)

The electric potential at b is given by,

Vb=kq1d1+kq2d2=kq1d1+q2d2=9脳1092.0脳10-60.0424-2.0脳10-60.03=-1.75KV

Therefore, the electric potential at b is -175 KV.

04

Work done on q3

(c)

The work done on charge q3 from a to b is given by,

W=q3Va-Vb=-5脳10-6175脳103-0=-0.875J

Therefore, the work done moving a charge from a to be is -0.875 Joules.

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