Potential Energy of a System of Charge: Definition, Formula, Solutions & Class 12 Notes

The total work done by external forces to bring charges from infinity to their current position without any acceleration is referred to as the potential energy of a system of charges. This concept helps to understand the interactions and stability of charged systems.

Important Links:

NCERT Class 12 Notes	Class 12 Chemistry notes
CBSE Class 12 Maths NCERT notes	Physcis Class 12 NCERT notes

If we are looking into the mathematical description, there is just one key aspect to know. Work done. The amount of work done for two charges separated at infinity to be brought somewhere closer is the potential energy of two point charges.

 

We will use this general formula.

$U=\frac{1}{4\pi {\epsilon }_0}·\frac{q_1{q}_2}{r}$

What are these variables?

•  U is the electrostatic potential charge
• R is the distance between two charges
• $q_1$ and $q_2$
• $\varepsilon_0$

Signs of U: When Charges Attract and Repel

• Positive potential energy (U > 0): When both charges are like charges, that tells us they are repelling each other
• Negative potential energy (U < 0): If the electrical charges have opposite signs, they are attracting each other.
  
  

 

The amount of work done to gather all charges from infinity to their current position without acceleration is expressed as the potential energy of multiple charges.

General Formula: 

System of n point charges q1​,q2​,q3​,…,qn​ placed at a distance of $r_{ij}$ from each other.

The potential energy U is: $U=\underset{i<j}{\sum }\frac{1}{4\pi {\epsilon }_0}·\frac{q_i{q}_j}{r_{ij}}$

Where,

• U is potential energy.
• $q_i\text{and}{q}_j$ are two charges in the system.
• $r_{ij}$ is the distance between the charges
• ε0​ is the permittivity of free space.

Also Check:

NCERT Class 12 notes	NCERT Class 12 Chemistry
Class 12 Maths NCERT notes	Physics Class 12 NCERT Notes