Electrostatic Potential Energy - Practice Questions & MCQ

Electrostatic Potential energy -

It is the amount of work done by external forces in bringing a body from  $\mathrm{\infty }$  to a given point against electric force.

or It is defined as negative work done by the electric force in bringing a body from  $\mathrm{\infty }$  to that point.

• - It is Scalar quantity
  - SI Unit: Joule
  - Dimension: $\left[M{L}^2{T}^{-2}\right]$

Electric Potential energy at a point

If the point charge Q is producing the electric field

Then electric force on test charge q at a distance r from Q is given by $F=\frac{KQq}{r^2}$
And the amount of work done by the electric force in bringing a test charge from $\mathrm{\infty }$ to $r$ is given by

$W={\int }_{\mathrm{\infty }}^r\frac{KQq}{x^2}dx=-\frac{KQq}{r}$

And negative of this work done is equal to electric potential energy

$\text{ So }U=\frac{KQq}{r}$

$U\to$ electric potential energy
$r\to$ distance between two
Change of potential energy-
if a charge q is moved from $r_1$ to $r_2$ in a electric field produced by charge Q
Then Change of potential energy is given as

$\mathrm{\Delta }U=KQq[\frac{1}{r_2}-\frac{1}{r_1}]$

$\mathrm{\Delta }U\to$ change of energy
$r_1,r_2\to$ distances
Potential Energy Of System Of two Charge-

$U=\frac{K{Q}_1{Q}_2}{r}(S.I{)}_{\text{where }}K=\frac{1}{4\pi {ϵ}_0}$
 

   Potential Energy For a system of 3 charges-

$U=K(\frac{Q_1{Q}_2}{r_{12}}+\frac{Q_2{Q}_3}{r_{23}}+\frac{Q_1{Q}_3}{r_{13}})$

Work energy relation-

$W=U_f-U_i$

Where $W=$ work done by an external force

$\begin{array}{rl}& U_f-\text{ final P.E }\\ & U_i-\text{ initial P.E. }\end{array}$

The relation between Potential and Potential energy-

$\begin{array}{rl}& U=\frac{KQq}{r}=q\left[\frac{KQ}{r}\right]\\ & \text{ As }\\ & \text{ But }=\frac{KQ}{r}\end{array}$

So $U=qV$
Or potential is defined as Potential energy Per unit charge.

$\text{ i.e }V=\frac{W}{Q}=\frac{U}{Q}$

Where $V\to$ Potential
$U\to$ Potential energy
Electron Volt-

$1\mathrm{ev}=1.6\times {10}^{-19}\mathrm{J}=1.6\times {10}^{-12}\mathrm{erg}$
 

It is the smallest practical unit of energy which is used in atomic and nuclear physics.

Electric potential Energy of Uniformly charged sphere-

$U=\frac{3Q^2}{20\pi {ϵ}_{0}R}$

Where R - Radius and Q - total charge.
Energy density- It is defined as the energy stored for unit volume.

$U_v=\frac{U}{V}$

Where $U-$ Potential Energy and $V-$ Volume.