Home
Class 12
PHYSICS
Derive an expression for potential energ...

Derive an expression for potential energy of a system of two charges in the absence of the external electrical field.

Text Solution

Verified by Experts


Imagine the charges `q_(1)andq_(2)` are initially at infinity. First the charge `q_(1)` is brought from infinity to the point A and no work is done for this. This is because there is no electric field to oppose this charges. Consider another point B at a distance r from A.
Electric potential at B due to `q_(1)` is given by,
`V_(1)=(1)/(4pirepsilon_(0))(q_(1))/(r)`
Next the charge `q_(2)` is brought from infinity to the point B. When the charge `q_(2)` is moved, the electric field due to `q_(1)` oppose it. Hence work has to be done.
Work done in bringing the charge `q_(2)` from infinity to the point B.
`W=V_(1)xxq_(2)`
This work done in stored in the charge as electric potential energy and given by,
`PE=u=(1)/(4piepsilon_(0)).(q_(1)q_(2))/(r)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the electric potential energy of the system of charges

Derive an expression for the rotational kinetic energy.

Define the term potential energy of charge q at a distance r in an external electric field.

In the absence of external magnetic field, d-orbital is

Define potential energy. Derive an expression for the potential energy of a body of mass m, at a height h above the surface of the Earth.

(a) Depict the equipotential surfaces for a system of two identical positive point charges placed a distance 'd' apart. (ii) Deduce the expression for the potential energy of a system of two point charges q_1 and q_2 brought from infinity of the points vecr_1 and vecr_2 respectively in the presence of external electric field vecE .

Answer the following: (a) Derive an expression for the potential energy of an electric dipole in a uniform electric field. Explain conditions for stable and unstable equilibrium. (b) Is the electrostatic potential necessarily zero at a point where the electric field is zero ? Give an example to support your answer.

Derive an expression for the gravitational potential energy of a body lying at a height above the surface of the earth.

Derive an expression for electric field intensity at a point due to point charge.

(a) Determine the electrostatic potential energy of a system consisting of two charge 7 muC and -2 muC (and with no external field) placed at (-9 cm, 0,0) and (9 cm, 0,0) respectively. (b) How much work is required to seperate the two charges infinitely away from each other ? (c) Suppose that the same system of charges is now placed in an external electric field E = A xx 1//r^(2) , where A = 9xx10^(5) C m^(-2) . What would the electrostatic energy of the configuration be ?