# What is the potential energy of a 3.2 nC charge placed at x = 0.5 m in units of nJ.

An infinite sheet of charge that has a surface charge density of 28 nC/m2 lies in the yz plane, passes through the origin, and is at a potential of 0.8 kV. A long wire having a linear charge density of 116 nC/m lies parallel to the y axis and intersects the x axis at 2m.

What is the potential energy of a 3.2 nC charge placed at x = 0.5 m in units of nJ.

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#### Solution Preview

Electric field on x-axis due to infinite sheet:

E(sheet) = s/2*ep

where, s (== sigma = surface charge density) =28 nC/m^2 =28*10^(-9) C

ep (== epsilon zero) = 8.86*10^(-12) C^2/N-m^2

therefore,

E = 28*10^(-9)/(2*8.86*10^(-12)) = 1.58*10^3 V/m

because,

dV = -E*dx

=> V = -E.x + constant

at ...

#### Solution Summary

Electric fields on an x-axis due to infinite sheet is examined. The potential energy for a charge is calculated. With good explanations, the formulas and calculations are shown in solving the problem.