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Question

Electric potential in a particular region of space is V=12x3x2y+2yz2. The magnitude of electric field at point P (1 m,0,2 m) in N/C is

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Solution

Given, Electric potential as
V=12x3x2y+2yz2
Ex=δVδx=126xy
and, Ey=δVδy=3x2+2z2
also, Ez=δVδz=4yz
E at (1,0,2) is given by
Ex=126×1×0=12
Ey=3×12+2×(2)2=5
Ez=4×0×(2)=0
E=12^i+5^j+0^k=12^i+5^j
and, |E|=122+52=13 N/C

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