Electric potential energy is own by an item by the virtue of 2 elements, those being, the fee possessed by an object itself and also the relative position of an item with respect to other electrically charged objects. The magnitude of electrical potential counts on the quantity of occupational done in relocating the thing from one allude to another against the electrical field.

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When an object is moved versus the electric field the gains part amount of energy which is characterized as the electric potential energy. For any type of charge, the electric potential is obtained by dividing the potential energy by the amount of charge.

### JEE key 2021 LIVE Physics record Solutions 24-Feb Shift-1 Memory-Based ## What is electric Potential Energy?

The electrical potential power of any given fee or mechanism of transforms is termed as the full work excellent by an external agent in pass the fee or the system of charges indigenous infinity to the existing configuration there is no undergoing any kind of acceleration.

Definition: electric potential power is identified as the full potential power a unit charge will certainly possess if located at any allude in the external space.

### Overview

Electric potential energy is a scalar quantity and also possesses only magnitude and no direction. It is measure in terms of Joules and also is denoted by V. That has the dimensional formula that ML2T-3A-1.

 Electric Potential Denoted by V, ∆V, U, ∆U Dimension: ML2T-3A-1 General Formula Voltage = Energy/Charge SI Unit Volt

There are two an essential elements on which the electrical potential power of an object depends.

It’s own electric charge.It’s relative position with other electrically fee objects.⇒ additionally Read:

## Electric Potential Formula:

A charge placed in an electrical field possesses potential energy and also is measured by the work-related done in relocating the charge from infinity to the point against the electrical field. If 2 charges q1 and q2 space separated by a distance d, the electric potential energy of the system is;

U = <1/(4πεo)> × If two prefer charges (two proton or 2 electrons) are lugged towards every other, the potential power of the system increases. If two unlike dues i.e. A proton and an electron are lugged towards each other, the electric potential energy of the mechanism decreases. ## Solved instances on electric Potential

Problem 1: A particle of mass 40 mg and carrying a fee 5×10-9 C is moving directly towards addressed positive point charge of size 10-8 C. When it is in ~ a street of 10 cm from the fixed allude charge it has actually a velocity that 50 cm/s. At what distance from the fixed suggest charge will certainly the particle come momentarily come rest? Is the acceleration continuous during motion?

Solution:

If the particle pertains to rest momentarily in ~ a street r native the addressed charge, from conservation of power we have,

Total energy of the system = Constant

(K.E + P.E) = constant

(1/2)mu2 + 1/4πεo × = (1/4πεo) × Substituting the provided data, we get;

⇒ 1/2 × 40 × 10-6 × 1/2 × 1/2 = 9 × 109 × 10-8 × 5 × 10-9 × < 1/r – 1/(10 × 10-2)>or, <1/r – 10> = (5×10-5)/(9×5×10-8) = 100/9

or, 1/r = (100/9) + 10 = 190/9 m

i.e., r = 4.7 × 10-2 m

Since, F = <1/4πεo> × Therefore, acceleration = F/m ∝ 1/r2 i.e., acceleration is not consistent during motion.

Problem 2: A ball of fixed 5 g and charge 10-7 C move from allude A who potential is 500 V come a suggest B who potential is zero. What is the velocity the the ball at allude A, if at suggest B, it is 25 centimeter per second?

Solution:

Let u it is in the velocity the the sphere at point A.

Workdone on the charge by the field;

W = q × (VA – VB) = 10-7 × (500 – 0) = 5 × 10-5 J

This shows up in indigenous of the enhanced kinetic energy.

∴ W = (1/2) mv2 – (1/2) mu2

5 × 10-5 = (1/2) × 5/1000 <(1/4)2 – u2>2 × 10-2 = 1/16 – u2

u2 = (1/16) – 0.02

= (1- 0.32)/16

= 0.0425

Therefore, u =0.206 m/s = 20.6 cm/sec.

Therefore, u = 20.6 cm/sec.

Example 3: Let us say we have two charges of magnitude 1C and also 2C placed at a distance 2 metre from every other. Calculation the electric potential between these two charges. (Take: k = 1)

Solution:

Given that, the magnitude of charges room q1 = 1C and also q2 = 2C.

The distance in between these 2 charges is r = 2m.

The electrical potential between these two charges is given by, Ur = -/r

Substituting the provided values in the above equation us get,

Ur = -1 J.

Example 4: How much work is compelled to it is in done, in order to lug two fees of magnitude 3C and also 5C native a separation of boundless distance come a separation that 0.5 m?

Solution:

∆E = E0 – Eg

= 0 – <-(9 × 109 × 5 × 3)/0.5> = 27 × 1010.

Therefore, ∆E = 27 × 1010.

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In an electrical circuit, the potential between two points (E) is defined as the quantity of job-related done (W) by an outside agent in relocating a unit fee (Q) from one allude to another.

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Mathematically we have the right to say that,

E = W/Q

Electric potential energy is characterized as the full potential energy a unit charge will possess if situated at any suggest in the external space.