A +45 μC point charge is placed 48 cm from an identical +45 μC charge. How much work would be required for an external force to move a +0.60 μC test charge from a point midway between them to a point 10 cm closer to either of the charges?
here,
magnitude of charge , q1 = 45 uC = 45 * 10^-6 C
sepration between charges , r = 48 cm = 0.48 m
q2 = 0.6 uC = 0.6 * 10^-6 C
x = 10 cm = 0.1 m
the work done required to move test charge from midway to 10 cm closer , W = change in potential energy
W = (2 * K * q1 * q2 /(r/2)^2) - ( K * q1 * q2 /(r/2 +x)^2 + K * q1 * q2 /(r/2 -x)^2)
W = 9 * 10^9 * 45 * 10^-6 * 0.6 * 10^-6 * ( 1/(0.48/2)^2 - ( 1/(0.24 - 0.10) + 1 /(0.24 + 0.10)))
W = 1.77 J
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