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/(4πεo) × [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, -∫ (ra→rb) F.dr = – (Ua – Ub)

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

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

As we know that Uinfity is equal to zero.

Therefore, -∫ (r →∞) F.dr = -UR

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

⇒ -∫ (r →∞) [-kqqo]/r2 dr = -UR

Or, -k × qqo × [1/r] = UR

Therefore, UR = -kqqo/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(r) = k× [qQ/r]

where, ke = 1/4πεo = Coloumb’s constant

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

U(r) = kq × ∑ni = 1  [Q/ri]

## 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,

• E = Electrical potential difference between two points,
• W = Work done in moving a change from one point to another,
• Q = Quantity of charge in coulombs.

### Solved Numericals of Electric Potentialand Potential Energy Nootan Solutions, Nageen Prakashan Kumar and Mittal

(page-110)

#### Question 1

The amount ………….at the point .

#### Question 2

How much………….. is 4 v ?

#### Question 3

5 J work………………… the Points .

#### Question 4

Compute electric…………..charge of ……… .

#### Question 5

A wire …….. at its center .

#### Question 6

Calculate in …………………. A to B , ( OA = 0.10 m ,………)

#### Question 7

A charge A ……………..From D to C ?

Question 8

Two charges ………………………….the Charges .

#### Question 9

The Potential …………distance of 0.4 m?

#### Question 10

The electric ……………of the charges .

#### Question 11

A point ………………… the point x …………..

Question 12

At each corner ……………………18 cm ?

#### Question 13

Electric charges …………………. of the square .

#### Question 14

10 J of …………………A and B ?

#### Question 15

……….. J of work ……………….the electric field .

#### Question 16

Two plane …………… two plates .

(page-111)

#### Question 17

The distance between ……………..to the order .

#### Question 18

How much kinetic ……………………answer in joule .

#### Question 19

An ..particle ……………………..J

(i)

(ii)

(iii)

#### Question 20

The mutual …………… the protons .

#### Question 22

Three point  ………….of the System .

Question 23

Three equal …………….. of charges .

#### Question 24

Two positive …………….. by 2 cm .

(i)…………

(ii)………….

#### Question 26

The distance between ……………..kinetic Energy ?

Question 27

Two electrons ………………between them ?

#### Question 28

Two point ………….equilibrium position .

#### Question 29

An Electric ………………….calculate .

(i)…………

(ii)………….

Question 30

Two point charges ………………….. dipole through  90 .

#### Question 31

Compare the electric ………………. silver is 47 .

#### Question 32

A hallow metallic ……………the sphere .

#### Question 33

A hallow spherical ……………….. of the Sphere .

(page-112)

#### Question 34

The Electric potential……………………the center .

#### Question 35

The electric potential…………………….of the sphere .

#### Question 36

Eight charged drop ……………….the bigger drop .

#### Question 37

27 identical drops ………………………..to be spherical .

#### Question 38

Calculate ……………………..drop is …………..and ………….

— End of Nootan Solutions Electric Potential and Potential Energy of Numericals :–

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