1)Two charges q 3 and q 4 which each have a magnitude of -1.85 ?C, half of that

Question

1)Two charges q3 and q4 which each have a magnitude of -1.85 ?C, half of that of q2. q1= 1.8?C, The charges are located a distance a = 2 cm from the oringin along the y-axis as shown. What is ?PE, the change in potential energy now if charge q1 is moved from point P to point R?

2)What is the potential energy of the system composed of the three charges q1, q3, and q4, when q1 is at point R? Define the potential energy to be zero at infinity.

3)The charge q4 is now replaced by charge q5 which has the same magnitude, but opposite sign from q4 (i.e., q5 = 1.85 ?C). What is the new value for the potential energy of the system?

Explanation / Answer

q3 = q4 = q = 1.85 uc

q1 = 1.8 uc

r1 = sqrt(a^2+d1^2)

r2 = sqrt(a^2+d2^2)

U1 = -k*q1*q3/r1 - k*q1*q4/r1

U2 = -k*q1*q3/r2 - k*q1*q4/r2

U2 - U1 = -k*q1*q3*(1/r2 - 1/r1) - k*q1*q4*(1/r2 - 1/r1)

dU = -(2*9*10^9*1.85*1.8*10^-12) * (1/sqrt(a^2+d2^2) - 1/sqrt(a^2+d1^2))

dU = -0.06 *(1/sqrt(a^2+d2^2) - 1/sqrt(a^2+d1^2))

2)

dU = U2 - U1

if d1 = infinity

U2 = -0.06 *(1/sqrt(a^2+d2^2)

3)

U1 = -k*q1*q3/r1 + k*q1*q5/r1

U2 = -k*q1*q3/r2 + k*q1*q5/r2

U2 - U1 = -k*q1*q3*(1/r2 - 1/r1 ) + k*q1*q5*(1/r2 - 1/r1)

U2 - U1 = 0

potential energy of the system = 0

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