Question

If electric potential in a region is represented by V= 2x+3y-4z obtain the expression fir potential gradient and electric field strength?

Answer 1

potential gradient is dV/ ds .

Answer 2

Answer:

The expression for potential gradient and the electric field strength is  1volt/m and -1 volt/m respectively.

Explanation:

From the question we have,

$V=2x+3y-4z$     (1)

The potential gradient is calculated as,

$G=\frac{dV}{ds}$     (2)

Where,

G=gradient of potential

V=potential

S=respective axis like x,y,z

Now,

$G=\frac{d(2x+3y-4z)}{dx}+\frac{d(2x+3y-4z)}{dy}+\frac{d(2x+3y-4z)}{dz}$

$G=2+3-4$

$G=1 Volt/m$     (3)

And the electric field is the negative potential gradient i.e.,

$E=-G$   (4)

So,

$E=-1 Volt/m$     (5)

Hence, the expression for potential gradient and the electric field strength is  1volt/m and -1 volt/m respectively.

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