Name: Electrostatic Potential Energy
Uploaded: 2019-07-19
Duration: 9 min 5 s
Description: Let's learn how a change in electrostatic potential energy is related to work done by an external force in moving a charge from one point to another in an el...

Question

Define electric potential at a point due to a charge and derive an expression for it.

Four charges $+ 2 C, - 2 C, + 2 C & - 2 C$ are placed at the four corners of a square $A B C D$ respectively. Find the resultant potential at the point of intersection of two diagonals.

Accepted Answer

The electrostatic potential at a point is measured by the work done to bring a unit charge from infinite distance to that point in the electric field.

Let us consider a point charge $q$ is present and $q_{o}$ is brought near it.

Then force experienced by this charge is $F = \frac{1}{4 π ε_{0}} \frac{q q_{o}}{x^{2}}$ .

Work done is given by, $W = \int F \cdot d x$

Here, $W = \int d W = - \int_{\infty}^{r} \frac{1}{4 π ε_{0}} \frac{q q_{o}}{x^{2}} d x$

$\Rightarrow W = \frac{1}{4 π ε_{0}} \frac{q q_{o}}{r}$

Electric potential is given as $V = \frac{W}{q_{o}} = \frac{1}{4 π ε_{0}} \frac{q}{r}$ .

Let us draw the diagram of a given problem as, let $P$ be the point at the centre.

Let $L$ be the distance from each charge to the point $P$ such that $A P = B P = C P = D P = L$ .

Electric potential due to $2 C$ be given by $V_{A} = \frac{1}{4 π ε_{0}} \frac{2}{L}$ and due to $- 2 C$ be given by $V_{B} = - \frac{1}{4 π ε_{0}} \frac{2}{L}$ .

Similarly, for other two points, $V_{C} = \frac{1}{4 π ε_{0}} \frac{2}{L}$ and $V_{D} = - \frac{1}{4 π ε_{0}} \frac{2}{L}$ .

Net potential at point $P$ is $V_{P} = \frac{1}{4 π ε_{0} L} [- 2 + 2 - 2 + 2] = 0$ .

Hence, potential at the point of intersection of diagonal is zero.

Define electric potential at a point due to a charge and derive an expression for it.

Four charges $+ 2 C, - 2 C, + 2 C & - 2 C$ are placed at the four corners of a square $A B C D$ respectively. Find the resultant potential at the point of intersection of two diagonals.

Important Questions on Electric Field and Potential

Learn and Prepare for any exam you want !

Define electric potential at a point due to a charge and derive an expression for it. Four charges +2 C,-2 C,+2 C & -2 C are placed at the four corners of a square ABCD respectively. Find the resultant potential at the point of intersection of two diagonals.

Important Questions on Electric Field and Potential

Learn and Prepare for any exam you want !

Define electric potential at a point due to a charge and derive an expression for it.

Four charges $+ 2 C, - 2 C, + 2 C & - 2 C$ are placed at the four corners of a square $A B C D$ respectively. Find the resultant potential at the point of intersection of two diagonals.