Tag: coulomb's law

Questions Related to coulomb's law

The most appropriate relationship between electric field and electric potential is given by

  1. $E = - \nabla V _E$

  2. $V _E = - \nabla E$

  3. $E = \nabla V _E$

  4. $V = - \nabla E$


Correct Option: A
Explanation:

$\vec{E}=-\dfrac{\partial V}{dx}\hat{i}-\dfrac{\partial V}{dy}\hat {j}-\dfrac{\partial V}{dz}\hat{k}$


And, we know that $\nabla=\dfrac{\partial}{dx}+\dfrac{\partial}{dy}+\dfrac{\partial}{dz}$

Hence, we get $\vec{E}=-\nabla V$

Answer-(A)

Electrostatic potential energy of a shell of radius $10cm.$ When $10C$ charge is distributed over its surface.

  1. $4.5 \times {10^{12}}J$

  2. $5.4 \times {10^8}J$

  3. $4.5 \times {10^9}J$

  4. $5.4 \times {10^6}J$


Correct Option: A
Explanation:

$U = \dfrac{{k\,Q \cdot Q}}{{2R}}$

    $ = \dfrac{{9 \times {{10}^9} \times 10 \times 10}}{{2 \times 0.1}}$
$U = 4.5 \times {10^{12}}J$