Electrostatic Potential Energy - Practice Questions & MCQ

Electrostatic Potential energy -

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

or It is defined as negative work done by the electric force in bringing a body from  $\infty$  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 $F=\frac{K Q q}{r^2}$
And the amount of work done by the electric force in bringing a test charge from $\infty$ to $r$ is given by

$
W=\int_{\infty}^r \frac{K Q q}{x^2} d x=-\frac{K Q q}{r}
$

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

$
\text { So } U=\frac{K Q q}{r}
$

$U \rightarrow$ electric potential energy
$r \rightarrow$ 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

$
\Delta U=K Q q\left[\frac{1}{r_2}-\frac{1}{r_1}\right]
$

$\Delta U \rightarrow$ change of energy
$r_1, r_2 \rightarrow$ 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 \epsilon_0}
$
 

   Potential Energy For a system of 3 charges-

$
U=K\left(\frac{Q_1 Q_2}{r_{12}}+\frac{Q_2 Q_3}{r_{23}}+\frac{Q_1 Q_3}{r_{13}}\right)
$

Work energy relation-

$
W=U_f-U_i
$

Where $W=$ work done by an external force

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

The relation between Potential and Potential energy-

$
\begin{aligned}
& U=\frac{K Q q}{r}=q\left[\frac{K Q}{r}\right] \\
& \text { As } \\
& \text { But }=\frac{K Q}{r}
\end{aligned}
$

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

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

Where $V \rightarrow$ Potential
$U \rightarrow$ 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{3 Q^2}{20 \pi \epsilon_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.