Nootan Solutions Electric Potential Energy ISC Physics Class-12 Nageen Prakashan

Nootan Solutions Electric Potential Energy ISC Physics Class-12 Nageen Prakashan Chapter-3 Solved Numericals. Step by step Solutions of Kumar and Mittal ISC Physics Class-12 Nageen Prakashan Numericsls Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Physics

Nootan Solutions Electric Potential Energy ISC Physics Class-12 Nageen Prakashan Chapter-3, Solved Numericals of Kumar and Mittal

Class:	12
Subject:	Physics
Chapter 3:	Electric Potential and Potential Energy

Board	ISC
Writer /Publications	Nootan / Nageen Prakashan/Kumar and Mittal
Topics	Solved Numericals of page 110 , 111,112

Definition

Electric potential energy is posses by an object by the virtue of two elements, those being, the charge possessed by an object itself and the relative position of an object with respect to other electrically charged objects. The magnitude of electric potential depends on the amount of work done in moving the object from one point to another against the electric field

When an object is moved against the electric field it gains some amount of energy which is defined as the electric potential energy. For any charge, the electric potential is obtained by dividing the potential energy by the quantity of charge

There are two key elements on which the electric potential energy of an object depends.

Its own electric charge,
Its relative position with other electrically charged objects.

Electric Potential Formula:

A charge placed in an electric field possesses potential energy and is measured by the work done in moving the charge from infinity to that point against the electric field. If two charges q₁ and q₂ are separated by a distance d, the electric potential energy of the system is;

U = 1/(4πε_o) × [q₁q₂/d]

Electric Potential Derivation

Let us consider a charge q₁. Let us say, they are placed at a distance ‘r’ from each other. The total electric potential of the charge is defined as the total work done by an external force in bringing the charge from infinity to the given point.

We can write it as, -∫ (r_a→r_b) F.dr = – (U_a – U_b)

Here, we see that the point r_bis present at infinity and the point r_ais r.

Substituting the values we can write, -∫ (r →∞) F.dr = – (U_r – U_∞)

As we know that U_infity is equal to zero.

Therefore, -∫ (r →∞) F.dr = -U_R

Using Coulomb’s law, between the two charges we can write:

⇒ -∫ (r →∞) [-kqq_o]/r² dr = -U_R

Or, -k × qq_o × [1/r] = U_R

Therefore, U_R = -kqq_o/r

Electric Potential of a Point Charge

Let us consider a point charge ‘q’ in the presence of another charge ‘Q’ with infinite separation between them.

U_E(r) = k_e× [qQ/r]

where, k_e = 1/4πε_o = Coloumb’s constant

Let us consider a point charge ‘q’ in the presence of several point charges Q_i with infinite separation between them.

U_E(r) = k_eq × ∑ⁿ_{i = 1} [Q_i/r_i]

Important Points

At a point midway between two equal and opposite charges, the electric potential is zero but the electric field is not zero.
The electric potential at a point is said to be one volt if one joule of work is done in moving one Coloumb of the charge against the electric field.
If a negative charge is moved from point A to B. The electric potential of system increases.
The reference level used to define electric potential at a point is infinity. It signifies that the force on a test charge is zero at the reference level.
The surface of the earth is taken to be at zero potential since the earth is so huge that addition or removal of charge from it will not alter its electrical state.

What is Electric Potential Difference?

In an electrical circuit, the potential between two points (E) is defined as the amount of work done (W) by an external agent in moving a unit charge (Q) from one point to another.

Mathematically we can say that,

E = W/Q

Where,