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The electric potential V at any point x,...

The electric potential V at any point x,y,z (all in metre) in space is given by `V=4x^2` volt. The electric field at the point `(1m, 0, 2m)` is ……………`V/m`.

Text Solution

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As electric field E is related to potential V through the relation
`E= -(dV)/(dr)`
`E_(x) = -(dV)/(dx) = -(d)/(dx) (4x^(2)) = -8x = 8 xx 1 =8`
`E_(y) = -(dV)/(dy) = -(d)/(dy) (4x^(2)) = 0`
And `E_(z) = -(dV)/(dz) = -(d)/(dz) (4x^(2)) = 0`
So, `vec(E ) = E_(x) hat(i) + E_(y) hat(j) + E_(z) hat(k) =-8x hat(i)`
at (1m, 0m, 2m) `vec(E ) = -8 hat(i)` i.e., it has magnitude 8V/m and is directed along negative x-axis
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