A point charge q 2 = -2.1 C is fixed at the origin of a co-ordinate system as sh

Question

A point charge q2 = -2.1 C is fixed at the origin of a co-ordinate system as shown. Another point charge q1 = 4.2 C is is initially located at point P, a distance d1 = 6.3 cm from the origin along the x-axis

1)

What is PE, the change in potenial energy of charge q1 when it is moved from point P to point R, located a distance d2 = 2.5 cm from the origin along the x-axis as shown?J

2)

The charge q2 is now replaced by two charges q3 and q4 which each have a magnitude of -1.05 C, half of that of q2. The charges are located a distance a = 1.5 cm from the origin 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?

Explanation / Answer

PE, the change in potenial energy of charge q1 when it is moved from point P to point R

= q1*(  V(1) - V(2)) ( V(1), V(2) are potential at point 2,1 due to charge 2, V due to q2 = Kq2/r)

=> PE = 4.2*10^-6 *( 9*10^9*2.1*10^-6 ( 1/(2.5*10^-2) -1/ (6.3*10^-2) ))

=> PE = 1.91 joule

part b

PE, the change in potenial energy of charge q1 when it is moved from point P to point R

= q1*(  V(1) - V(2)) ( V(1), V(2) are potential at point 2,1 due to charge 3,4 V due to each q3,q4 = Kq/r)

r1 = sqrt ( a^2 +d1^2) = sqrt( 1.5^2 + 6.5^2) = 6.67cm

r2 = sqrt ( a^2 +d2^2) = sqrt ( 1.5^2 + 2.5^2) = 2.91cm

=> PE = 4.2*10^-6*( 9*10^9*2.1*10^-6)* ( 1/(2.91*10^-2) -1/ (6.67*10^-2) ))

=> PE = 1.53Joule

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