Question

Two point charges Q1 = +4.10 nC and Q2 = −2.40 nC are separated by 55.0 cm. (a) What is the electric potential at a point midway between the charges? 55.57 Correct: Your answer is correct. seenKey 55.6 V (b) What is the potential energy of the pair of charges? -1.61E-7 Correct: Your answer is correct. seenKey -1.61e-07 J What is the significance of the algebraic sign of your answer? correct Positive work must be done to separate the charges. Negative work must be done to separate the charges. Correct: Your answer is correct.

Answer 1

A) V = 55.57 V

B) E = -1.61 x 10^(-7)J

C) Negative sign means that positive work must be done to separate the charges (bring them up to a state of zero potential energy)

Step-by-step explanation:

A) Electric potential is given by the formula;

V = KQ/d

Since there are two charges and we are looking for the electric potential at a point midway through them, we now have;

V = kQ1/0.5d + kQ2/0.5d

This can be arranged as;

V = (k/0.5d)(Q1 + Q2)

Where;

k is coulombs constant and has a value of 8.99 x 10^(9) N.m²/C²

d = 55 cm = 0.55m

Q1 = +4.10 nC = 4.1 x 10^(-9) C

Q2 = −2.40 nC = -2.4 x 10^(-9) C

Thus;

V = (8.99 x 10^(9))/(0.5 x 0.55)[4.1 x 10^(-9) - 2.4 x 10^(-9)]

V = 55.57 V

B) The formula for the potential energy of the pair of charges is;

E = kQ1•Q2/d

Thus, E = [(8.99 x 10^(9)) * 4.1 x 10^(-9) * -2.4 x 10^(-9)]/0.55

E = -160.8 x 10^(-9)

Or

E = -1.61 x 10^(-7)J

C) Negative sign means that positive work must be done to separate the charges (bring them up to a state of zero potential energy)