Question

Define electric potential.

Then find expression for electric potential due to a point charge at any arbitrary point.

< Class 12th >
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Answer 1

Defination :-

Electric potential at a point may be defined as Work done in bringing a unit positive test charge from infinity to that point without changing kinetic energy.

⇝ In Attached Figure :-

• q = Point charge due to which electric potential is to be find.

• $\sf+ q_ \circ$ = +ve Test charge

• P = Any point where potential is to be find.

⇝ Derivation :-

[ Figure in Attachment ]

Small work done to move charge from point P to infinity is :

$\text{dW = - F.dx}$

$:\longmapsto\text{dW} = - \frac{\text{kqq}_{\circ}}{\text x {}^{2} }$

⏩ Integrating Both Side ;

$\text{W}_{\text P\rightarrow \infty } = - \int\limits^ \infty _\text r \text{kqq}_{\circ}( {\text x}^{ - 2} ) \ \text {dx}$

$= - \text{kqq}_{\circ} {{\bigg[ - \frac{1}{\text x} \bigg]}_\text r^ \infty }$

$\text{W}_{\text P \rightarrow \infty } = - \frac{\text{kqq}_{\circ}}{\text r}$

$\large\red{\therefore \: \boxed{ \boxed{\text{W}_{\infty \rightarrow\text P } = \frac{\text{kqq}_{\circ}}{\text r} }}}$

⏩ By Defination :

$:\longmapsto \rm V_P=\frac{ W_{\infty \rightarrow P} }{q_{\circ}}$

$:\longmapsto \rm V_P = \frac{{kqq}_{\circ}}{rq_{\circ}}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf V_P = \frac{{kq}}{r}} }}}$

which is electric potential due to a point charge at point P.

Answer 2

Answer:

Given:-

• Question:-

1. Define electric potential
2. Find expression for electric potential due to a point charge at any arbitrary point .

□Lets,

• In the question that first we should write the defination of electric potential.

$electric \: potential \: is \: defined \: as \: the \: work \: done \: in \: which \: a \: unit \: positive \: test \: it \: changes \: from \: infinity \: to \: that \: without \: changing \: of \: kinetic \: energy$

♧Derivation:-

• Here to get answer u refer the give attachment for more information.
• That will helps you .

□Conclusion :-

• If u got any problem in this answer refer the above Brainly best user answer that also will helps you a lot .

♧Hope it helps u mate .

♧Thank you.