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Question

If E=(2y33yz2)^x(6xy23xz2)^y+(6xyz)^z is the electric field in a source free region, a valid expression for the electrostatic potential is

A
xy3yz2
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B
2xy3xyz2
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C
y3+xyz2
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D
2xy33xyz2
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Solution

The correct option is D 2xy33xyz2

Ans : (d)

E=Vx^axVy^ayVZ^az

Vx=2y23yz2V=2xy33xyz2+K1

Vy=6xy23xz2V=2xy33xyz2+K2

Vz=6xyzV=3xyz2+K3
Comparing all three for uniqueness solution of potential

K1=K2=0K3=2xy3

E=(2y33yz2)^x(6xy23xz2)^y+(6xyz)^z

as we know that E=V

E=(x^x+y^y+z^z)V ... (i)
Clearly option (d) satisfies the given relation.


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