Question

The electric potential at a point is given by V = z(z2 - 4x2). Calculate the electric field E at that point.​

Answer 1

Given:

• The electric potential at a point is given by $V = z(z^2 - 4x^2)$

To Find:

• Calculate the electric field E at that point.

Solution:

  The electric field E at a point given as

            $\overrightarrow E = -( \frac{\delta }{\delta x} \hat{i} + \frac{\delta }{\delta y} \hat{j} +\frac{\delta }{\delta z} \hat{k} ) V$

         $V = z(z^2 - 4x^2)$

  ⇒          $d.w.r \ to \ x$

            $\frac{\partial V}{\partial x}=-8zx$

Now,

     ⇒    $d.w.r \ to \ y$

            $\frac{\partial V}{\partial y}=0$

    ⇒         $d.w.r \ to \ z$

               $\frac{\partial U}{\partial z}=3z^2-4x^2$

Now, Electric field at the point

            $\overrightarrow{E}=(8zx)\cdot\overrightarrow{i}-(3z^2-4x^2)\cdot \overrightarrow{k}$