➤ Potential Energy of a Single Charge
Potential energy of q at r in an external field:
U = q.V(r),
where V(r) is the external potential at the point r.
➤ Potential Energy of a System of two Charges in an External Field
First, we calculate the work done in bringing the charge q_{1} from infinity to r_{1}.
Next, we consider the work done in bringing q_{2} to r_{2}. In this step, work is done not only against the external field E but also against the field due to q_{1}.
_{Thus, }_{Potential energy of the system }_{= Total work done in assembling the configuration}
_{⇒ Potential Energy of the System}
➤ Electric Potential Energy of a Dipole in an External Field
We thus obtain:
➤ Electric Potential Energy of a System of Two Charged Particles
➤ Electric Potential Energy for a System of Multiple Charged Particles
➤ Electric Potential Due to a Conducting Sphere or a Shell
➤ Electric Potential Due to Solid NonConducting Sphere
➤ Electric Potential Due to a Uniformly Charged Rod
Electric Potential due to a uniformly charged rod of length L and linear charge density lambda, at a point P on its axial line which is d units away from it.Charge per unit length, λ = Q/L
Charge of slice, dq = λ.dx
Thus, Electric potential due to uniformly charged rod:
➤ Electric Potential Due to a Charged Ring
Let electric potential at point P due to small element of length dℓ be dV.
(distance between small element and point P is equal to r)
Thus, Electric potential due to whole ring:
➤ Potential Due to a Uniformly Charged Disc
Find the electric potential at the axis of a uniformly charged disc and use potential to find the electric field at same point.Thus, Electric Potential due to ring element of radius r and thickness dr is dv:
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