System of Charges

What is electric potential? 

No charge can exist individually, and hence every conductor or material experiences a system of charges. Electric charge and its associated concepts are always viewed in a set of charges. Thus, electric energy or electric potential energy is defined as the work done by a charge to change its position in the electric field. It depends on the initial and final position of the charge and is highly independent of the path taken by the system of charges. It is easy to calculate this energy in the system of charges. Let there be a system of two point charges  p and q, where p moves in the electric field produced by q. Here q is the fixed point, and it is displaced, such that r₁ is the distance between p and the common point s while r₂ is the distance between q and the common point s. Thus, dW= F.dr where dr is the small displacement of the force and dW is the work done. The work done in moving the charge q from its position to s equals the change in the potential energy required to move q from its position to s. Hence, W= U (r₁) – U(r₂) Here,

• U (r₁) is the potential energy of the charge q when it is at a fixed point; and
• U (r₂) is the potential energy of the charge q when it reaches position s.

Superposition principle:

The superposition principle gives the value of net force on any charge. It states that the net force on a charge in an electrical field is equal to the vector sum of all the forces on the charge. However, all these individual forces are unaffected by the presence of the other charges. If there are n number of charges in a system. Then Net force F (net) is F(net)= F₂₁ + F₃₁+ F₄₁+ F₅₁+ ….+ F_n1

Electric potential energy:

The calculation of the electric potential is done by the principle of superposition. Hence, the net potential on the charge in an electrical field equals the sum of all individual potentials. Hence,  V (net) = V₁+ V₂+ V₃+ V₄+ …..+ V_n Or  V (net)= k( q1/r₁ + q₂/r₂+ q₃/r₃+..+ q_n/r_n)

The potential energy of a system of two point charges:

The potential energy is from the collection of charges when all these charges in the system create a force on each other. Hence, this potential energy is the total amount of work done in moving the system of charges from discret distances to their respective positions in the system. Thus, U (E) = kq₁q₂r₁₂  Where r₁₂ is the position vector between two charges, q₁ and q₂.

SI unit of charge

The unit of electric charge measurement is one Coulomb in the MKS system. It is the basis of the SI system. SI unit of charge is Coulomb or C. One Coulomb is defined as the amount of electricity transported by one Ampere current in one second. The charge SI unit i.e., one coulomb is equal to the charge on 6.242 X1018 protons. The SI system defines Coulomb using the amperes and seconds.

CGS unit of charge

The CGS unit of charge is “esu”. It is also called “stat coulomb” and is defined as the electrostatic force between two equal point charges that are one centimetre apart.

Conclusion:

So, the system of charges makes an important part of the physics syllabus for the IIT-JEE examination. Understanding the details of electric charge, the units to measure the charges, and the effect of this system is extremely necessary.