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The electric potential existing in space...

The electric potential existing in space is `V(x,y,z)= A (xy+ yz+zx)`.(a) Write the dimensional A. (b) find the expression for the electric field.( c ) If A is 10 SI units, find the magnitude of the electric field at (1m, 1m, 1m).

Text Solution

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`V= B (xy + yz + zx)`
`E_(x) = (-del V)/(del x) = -B(y+z)`
because variables y and z are treated as constant Now, put the values of B, y and z. Given B = 10 and (x,y,z) are (1,1,1) respectively.
So, `E_(x) = (-del V)/(del x) = -B (y+z) = -10 (1 + 1) = -20N//C`
Similarly, `E_(y) = (-del V)/(del y) = -B (x + z)` [now treating x and z are constants] therefore `E_(y) = - 10 (1 +1) = -20N//C and E_(z) = (-del V)/(del z) = -B(x + y) = -20N//C`
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