Prove that electrostatic forces are conservative in nature and define electrostatic potential energy

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2. Electric Potential and Capacitance

medium

Prove that electrostatic forces are conservative in nature and define electrostatic potential energy.

Option A

Option B

Option C

Option D

Solution

When an external force does work in taking a charge from a point to another against a electrostatic force the work gets stored as potential energy of the charge and when the external force is removed the charge moves gaining kinetic energy and losing an equal amount of potential energy. The sum of kinetic and potential energies is thus conserved and hence electrostatic forces are conservative in nature.

Definition of electrostatic potential energy : "The work done in a direction, opposing the electric field in bringing a unit positive charge with constant speed from an infinite position to any point in the electric field is called the static electric potential energy at that particular point".

Standard 12

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hard

(AIPMT-2007)

There exists a uniform electric field $E=4 \times 10^5 \,Vm ^{-1}$ directed along negative $x$-axis such that electric potential at origin is zero. Acharge of $-200 \,\mu C$ is placed at origin, and a charge of $+200 \,\mu C$ is placed at $(3 \,m , 0)$. The electrostatic potential energy of the system is ………..$J$

medium

There is $10$ units of charge at the centre of a circle of radius $10\,m$. The work done in moving $1\, unit$ of charge around the circle once is………..$units$

easy

(AIIMS-2000)

Prove that electrostatic forces are conservative in nature and define electrostatic potential energy.

Solution

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