Electric Potential due to a point charge: Overview, Questions, Preparation

Q: Q: A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor

A: Capacitance C = 12 pF = 12 × 10−12 F Potential difference, V = 50V Electrostatic energy stored in the capacitor is given by the relation, E = 1/2 C?2 = 1/2×12 × 10−12 × (50)2 J = 1.5 × 10−8 J

Rajdeep Das

Updated on Aug 25, 2021 01:17 IST

Table of Contents

What is Electric Potential?
Factors of Electric potential of an object
Electric Potential due to Point Charge
Electric potential due to Multiple Charges
Electric potential due to a point charge for Class 12
FAQs

What is Electric Potential?

Electric Potential is the concept defined as the work needed to move one unit charge to a specific unit charge against the electric field of the work. By moving it against the electric field, the object gained a significant amount of energy which is known as electric potential energy.

The electric potential is the relationship between the potential energy and the quantity of charge. It can be calculated using the following formula:

E = W / Q

Here, E is the electric potential of the charge,

W is the potential energy,

Q is the quantity of charge.

Factors of Electric potential of an object

The electric potential of an object depends on some external factors which are as follows:

It is dependent upon the electric charge that an object carries,
Another factor responsible for the electric potential charge of an object is the relative position of an electrically charged object.

Electric Potential due to Point Charge

It is defined as the relationship between the position vector of the positive charge object and the source change. The amount of work done on a positive charge object to infinity when external electrostatic forces apply on the object is known as Electric potential due to a point change. The equation of the electric potential due to point change is given below:

V = 1 / 4πϵ0 q / r

Here, change in the source is denoted as q,

The positive charge of the position vector is denoted as q

V is the electric potential due to point change.

The unit used to measure the electric potential is Volt,

So, 1 volt = 1 joule coulomb (JC-1)

Electric potential due to Multiple Charges

I can write the electric potential due to multiple charges as:

V = KQ1 / r1 + KQ2 / r2 + KQ3 / r3

There are 3-point charges, and the distance is r1, r2, and r3. The point charges are denoted as q1, q2, and so on.

It is used to determine the electrostatic potential of multiple points by adding all the individual point charges.

Electric potential due to a point charge for Class 12

The chapter 'Electric Charge' holds a weightage of 14 marks, making it the most important chapter in Physics. It included six questions in total, consisting of 2 objective type questions of 1 mark each, two very short questions of 2 mark each, one short question of 3 marks, and lastly one long question of 5 marks.

Illustrative Examples

Example 1) State the formula used to find the electric potential difference?

Answer – The formula used to find the potential difference is E = W / Q

Example 2) Write one factor of the electric potential of an object.

Answer – The factor of the electric potential of an object is that it is dependent upon the electric charge that an object carries.

Example 3) Write the formula of electric potential due to multiple charges.

Answer – The formula of electric potential due to they wrote multiple charges below:

V = KQ1 / r1 + KQ2 / r2 + KQ3 / r3

FAQs

Q A small sphere of radius r1 and charge q1 is enclosed by a spherical shell of radius r2 and charge q2. Show that if q1 is positive, charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge q2 on the shell is.

A: According to Gauss’s law, the electric field between a sphere and a shell is determined by the charge ?1 on a small sphere. Hence, the potential difference, V, between the sphere and the shell is independent of charge ?2. For positive charge ?1, potential difference V s always positive.

Q Describe schematically the equipotential surfaces corresponding to (a) a constant electric field in the z-direction, (b) a field that uniformly increases in magnitude but remains in a constant (say, z) direction, (c) a single positive charge at the origin, and (d) a uniform grid consisting of long equally spaced parallel charged wires in a plane.

A: Equidistant planes parallel to the x-y plane are the equipotential surfaces.
(b) Planes parallel to the x-y plane are the equipotential surfaces with the exception that when the planes get closer, the field increases
(c) Concentric spheres centered at the origin are equipotential surfaces.
(d) A periodically varying shape near the given grid is the equipotential surface. This shape gradually reaches the shape of planes parallel to the grid at a larger distance.

Q: A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor

A: Capacitance C = 12 pF = 12 × 10_⁻¹²F
Potential difference, V = 50V
Electrostatic energy stored in the capacitor is given by the relation,
E = 1/2 C?_² = 1/2×12 × 10_⁻¹² × (50)_² J = 1.5 × 10_⁻⁸ J

Q: What do you mean by electric potential?

A: Electric Potential is the concept defined as the work needed to move one unit charge to a specific unit charge against the electric field of the work.

Q: Write the SI unit of electric potential.

A: The SI unit of electric potential is Joules per Coulomb.

Q: What is electric potential due to point charge?

A: It is defined as the relationship between the position vector of the positive charge object and the source change

Q: Is potential energy a scalar or a vector quantity?

A: The potential energy is a scalar quantity.

Q: Which device is used to measure the difference in electric potential?

A: Voltmeter is used to find the difference.