Question 1: Two point charges +Q and ?Q are arranged as shown in the scale diagr

Question

Question 1: Two point charges +Q and ?Q are arranged as shown in the scale diagram at right. Points A, B, C. and D are locations near the charges. Each square on the grid has length and width a. The electric potential infinitely far away from these charges is set to zero. a) Is the magnitude of the electric field at point B greater than, less than, or equal to the magnitude of the electric field at point D? Explain. b) Is the absolute value of the electric potential at point B greater than, Less than or equal to the absolute value of the electric potential at point D? Explain. c) Is the absolute value of the electric potential at point B greater than, Less than or equal to the absolute value of the electric potential at point C? Explain. d) A positive test charge +q moves from point B to point D. Is the work done by the electric field on the test charge positive, negative, or zero? Explain. e) A positive test charge +q moves from point B to point A. and then from point A to point D). Is the work done by the electric field on this charge greater than, less than, or equal to the work done in part d)?

Explanation / Answer

Distance between + Q and D = r1 = sqrt((4a)^2 + (2a)^2) = sqrt(20) a

Distance between - Q and D = r2 = sqrt((4a)^2 + (2a)^2) = sqrt(20) a

r1 = r2 = r

Distance between + Q and B = r1 = 3a

Distance between - Q and B = r2 = 3a

r1 = r2 = r = 3a

a) magnitude of electric field at B = k Q / r1^2 + k Q / r2^2 =    k Q / 9a^2 + k Q / 9a^2 = 2 k Q / 9a^2 =

0.22 k Q/a^2

magnitude of electric field at D = k cos(arctan(0.5)) Q / 20a^2 + kcos(arctan(0.5)) / 20a^2 = 0.0894 k Q / a^2

magnitude is same

b)

absoulte value of potential at B = k Q / r1 - k Q / r2 =    k Q / 3a - k Q / 3a = 0

absolute value of potential at D =  k Q / r1 - k Q / r2 =  k Q / sqrt(20)a - k Q / sqrt(20)a = 0

absolute value is same

c) potential at B = 0

potential at C = kQ/6a - k Q/2a = - k Q / 3a

Absolute value of potential at B is greater than at C

d) Since potential at B and D are equal

work done by electric field = 0

e) Work done depends on final and initial position of test charge , independent of the path

Final position is D

Initial position is B

Since potential at B and D are same

Work done = 0

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Answers

a) greater than

b) equal

c) greater

d) zero

e) equal

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