The electric potential at a point (x, y, z) is given by V = - x²y - xz³ + 4 The electric field at that point is:

Question

Question

Answer 1

CONCEPT:

Electric Potential: The work done per unit positive charge in bringing a charged particle from infinity to that point is electric potential.
Electric Field is a vector quantity that is defined as the change in potential difference per unit displacement.

The electric field at a given point in space with Coordinate (x, y, z) having potential V is given as

CALCULATION:

Given V = x2y - xz3 + 4

Now,

⇒ ---- (1)

⇒

⇒ ------- -- --(2)

⇒

⇒ ------- - (3)

Putting (1), (2) and (3) in Equation of Electric Field.

⇒

So, this is the required expression for the electric field.

Important Points

∂ operator is used for partial differentiation. If the partial differentiation is done with respect to a variable, the other variables are considered as constant and differentiation is done accordingly.

Example:-

Here, differentiation is done with respect to x. So, y and z are considered as constant.