Question

If the potential in a region of the electric field is expressed as V(x, y, z) = 2xy + 3zx - yz, then the electric field at point (0, 1, 1) is ______.

विकल्प

• `-hati + 5hatj - 3hatk`

• `hati - 5hatj + hatk`

• `5hati + hatj + hatk`

• `-5hati + hatj + hatk`

Answer 1

If the potential in a region of the electric field is expressed as V(x, y, z) = 2xy + 3zx - yz, then the electric field at point (0, 1, 1) is `underlinebb(-5hati + hatj + hatk)`.

Explanation:

Given, V = 2xy + 3zx - yz

∴ Electric field, E = `-(dV)/(dx)hati - (dV)/(dy)hatj - (dV)/(dz)hatk`

= `(-2y - 3z)hati - (2x - z)hatj - (3x - y)hatk`

`E_{at(0, 1, 1)} = (-2 - 3)hati - (0 - 1)hatj - (0 - 1)hatk`

= `-5hati + hatj + hatk`