Question

The electric potential V at any point O (x, y, z all in metres) in space is given by V = 4x² volt. The electric field at the point (1 m, 0, 2m) in volt/metre is ____________.

Options

• 8 along negative X - axis

• 8 along positive X - axis

• 16 along negative X - axis

• 16 along positive Z- axis

Answer 1

The electric potential V at any point O (x, y, z all in metres) in space is given by V = 4x² volt. The electric field at the point (1 m, 0, 2m) in volt/metre is 8 along negative X - axis.

Explanation:

`"The electric potential V (x, y,z)" = 4 "x"^2  "volt"`

`"Now"  vec "E" = - (hat "i" (del "V")/(del "x") + hat "j"(del "V")/(del "y") + hat "k" (del "V")/(del "z"))`

`"Now"  (del "V")/(del "x") = 8 "x", (del "V")/(del "y") = 0 and (del "V")/(del "z") = 0`

`"Hence"  vec "E" = -8 "x"  hat "i"`

so at point (1m, 0, 2m)

`vec "E" = -8  hat "i"  "volt / metre or 8 V/m along negative X-axis"`