Last Updated on August 2, 2024 by XAM CONTENT

Hello students, here you will find numerical on electric potential with answers. Before we start solving the numerical, let’s see some important points and formulae. This will help you to solve the problems efficiently.

### Understanding Electric Potential

Electric potential is a fundamental concept in physics that helps us understand how electric charges interact in an electric field. Think of it as the “electric pressure” that pushes charges around, much like how water pressure pushes water through pipes.

Imagine you have a hill, and you place a ball at the top. The higher the hill, the more potential energy the ball has because gravity will cause it to roll down. Similarly, in an electric field, electric potential is the energy per unit charge that a charge would have due to its position.

To break it down further, let’s use an analogy. Consider a water slide at a theme park. The higher you go up the slide, the more potential energy you have because you’ll go faster and farther when you slide down. In the same way, if you place a positive charge near another positive charge, it will have high electric potential energy because like charges repel each other, and you would need to do work to bring them close together.

### Electric Potential due to Point Charge

Consider a positive point charge q placed at the origin O. We wish to calculate its electric potential at a point P at distance r from it, as shown in Fig.

By definition, the electric potential at point P will be equal to the amount of work done in bringing a unit positive charge from infinity to the point P.

Suppose a test charge q_{0} is placed at point A at distance x from O. By Coulomb’s law, the electrostatic force acting on charge q_{0} is

The total work done in moving the charge q_{0} from infinity to the point P will be

Hence the work done in moving a unit test charge from infinity to the point P, or the electric potential at point P is

A higher electric potential means that more work is required to bring a unit positive charge from infinity to that point. It also indicates a stronger electric field around that point, causing charges to experience greater force.

In the below section, we are providing numerical problems based on Electric Potential for Class 12 Physics.

### Electric Potential Class 12 Physics Numerical with Answers

**Formula used:**

1. Potential difference

2. Electric potential due to a point charge q at distance r from it,

3. Electric potential at a point due to N point charges,

4. Electric potential at a point due to a dipole,

**Units used:**

Charge q is in *coulomb*, distance r in *metre*, work done W in *joule *and potential difference V in *volt*.

Question 1: If 100 J of work has to be done in moving an electric charge of 4C from a place, where potential is -10 V to another place, where potential is V volt, find the value of V.

Ans. 15 V

Question 2: (i) Calculate the potential at a point P due to a charge of 4 × 10^{-7} C located 9 cm away, (ii) Hence obtain the work done in bringing a charge of 2 × 10^{-9} C from infinity to the point P. Does the answer depend on the path along which the charge is brought?

Ans. (i) 4 × 10^{4} V (ii) 8 × 10^{-5} J

No, the answer does not depend on the path along which the charge is brought.

Question 3: A metal wire is bent in a circle of radius 10 cm It is given a charge of 200 μC which spreads on it uniformly. Calculate the electric potential at its centre.

Ans. 18 x 10^{6} V

Question 4: Two charges 3 × 10^{-8} C and – 2 × 10^{-8} C are located 15 an apart. At what point on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

Ans. 9 cm and 45 cm away from the positive charge on the side of the negative charge.

Question 5: Two charges -q and +q are located at points A (0, 0, -a) and B (0, 0, +a) respectively. How much work is done in moving a test charge from point P (7, 0, 0) to Q (-3, 0, 0)?

Ans. zero

Explanation: Points P and Q are located on the equatorial line of the electric dipole and potential of the dipole at any equatorial point is zero.

Question 6: The work done in moving a charge of 3 C between two points is 6J. What is the potential difference between the two points?

Ans. 2 V

We hope the given numerical on Electric Potential for Class 12 Physics helps you in your learning.

### Also check

- Electric Potential Class 12 Physics Numerical with Answers
- Superposition Principle of Electric Forces Class 12 Physics Numerical with Answers

### Frequently Asked Questions (FAQs) on Electric Potential Class 12 Physics

#### Q1: **What is electric potential?**

A1: Electric potential is the amount of electric potential energy per unit charge at a point in an electric field. It is a measure of the work done to move a unit positive charge from infinity to that point. The unit of electric potential is the volt (V).

#### Q2: **How is electric potential different from electric potential energy?**

A2: Electric potential is the potential energy per unit charge at a point in an electric field, while electric potential energy is the total energy a charge has due to its position in the field. Electric potential is measured in volts (V), whereas electric potential energy is measured in joules (J).

#### Q3: **What is the formula for electric potential?**

A3: The formula for electric potential (V) at a point is given by: *V = W/q*, where W is the work done to move the charge q

q from infinity to that point.

#### Q4: **What is the unit of electric potential?**

A4: The unit of electric potential is the volt (V). One volt is defined as one joule per coulomb (1 V = 1 J/C).

#### Q5: What is the relationship between electric potential and electric field?

A5: The electric field (E) is the negative gradient of the electric potential (V). This means the electric field is the rate of change of the electric potential with respect to distance.

#### Q6: **How do you calculate the electric potential due to a point charge?**

A6: The electric potential (V) due to a point charge (Q) at a distance (r) from the charge is given by: *V = kq/r*, where k is Coulomb’s constant.

#### Q7: Can electric potential be negative?

A7: Yes, electric potential can be negative. This occurs when work is done by the electric field (rather than against it) to bring a unit positive charge from infinity to that point. Negative potential typically happens near negative charges or in regions where the electric field direction opposes the movement of positive charges.

#### Q8: What is the difference between electric potential and voltage?

A8: Electric potential is the energy per unit charge at a point, while voltage is the difference in electric potential between two points. Voltage is what drives electric current in a circuit and is also measured in volts (V).

#### Q9: How do batteries relate to electric potential?

A9: Batteries create a potential difference (voltage) between their terminals. This potential difference provides the energy needed to move charges through a circuit, powering electrical devices. The voltage of a battery is a measure of the electric potential difference it can provide.