Name: The Relation Between Electric Field and Potential
Uploaded: 2019-07-19
Duration: 10 min 41 s
Description: The electric field is the electric force per unit charge, and the electric potential is the work done per unit charge. Is there any relation between electric...

Question

A solid sphere of the radius $R$ has a cavity of radius $\frac{R}{2} .$ The solid part has a uniform charge density $ρ$ and cavity has no charge. Find the electric potential at the point $A$ . Also, find the electric field (only magnitude) at a point $C$ inside the cavity.

Accepted Answer

We can solve the problem with negative charge concept. First, we fill the cavity with a positive charge and make a full complete spherical body. And then we assume a negatively charged body exactly of shape and position of the cavity and placed where the cavity is.

Assume we have filled the cavity.

Now, the electric potential at $A$ due to this solid sphere,

$A$

Here, $Q = ρ \times volume of sphere$ .

$∴ V_{A} = \frac{3}{2} \cdot \frac{1}{4 π ε_{0}} \frac{(\frac{4}{3} π R^{3} ρ)}{R} = \frac{ρ R^{2}}{2 ε_{0}}$

Now consider the cavity filled with a negative charge. Potential due to this at the point $A$ is

$V_{A}^{'} = \frac{K Q^{'}}{(\frac{R}{2})}$

Here, $Q^{'} = - ρ \times volume$ .

$\frac{R}{2} .$

Potential is a scalar quantity and can be added directly.

$∴ V_{A} = V_{A}^{} + V_{A}^{'} = \frac{ρ R^{2}}{ε_{0}} (\frac{1}{2} - \frac{1}{12}) = \frac{5 ρ R^{2}}{12 ε_{0}}$

For cavity, we know that the electric field in the whole cavity is uniform. Using the formula,

${\vec{E}}_{C} = \frac{ρ \vec{A B}}{3 ε_{0}} |{\vec{E}}_{C}| = \frac{ρ (\frac{R}{2})}{3 ε_{0}} = \frac{ρ R}{6 ε_{0}}$

A solid sphere of the radius $R$ has a cavity of radius $\frac{R}{2} .$ The solid part has a uniform charge density $ρ$ and cavity has no charge. Find the electric potential at the point $A$ . Also, find the electric field (only magnitude) at a point $C$ inside the cavity.

Important Questions on Electric Potential

Learn and Prepare for any exam you want !

A solid sphere of the radius R has a cavity of radius R2. The solid part has a uniform charge density ρ and cavity has no charge. Find the electric potential at the point A. Also, find the electric field (only magnitude) at a point C inside the cavity.

Important Questions on Electric Potential

Learn and Prepare for any exam you want !

A solid sphere of the radius $R$ has a cavity of radius $\frac{R}{2} .$ The solid part has a uniform charge density $ρ$ and cavity has no charge. Find the electric potential at the point $A$ . Also, find the electric field (only magnitude) at a point $C$ inside the cavity.