We have to keep this in mind.
Answers
Answer:
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.
\large\sf+ q_ \circ+q
∘
= +ve Test charge
P = Any point at distance r where potential is to be find.
\large \dag† Derivation :-
[ Figure in Attachment ]
Small work done to move charge from point P to infinity is :
\begin{gathered} \text{dW = - F.dx} \\ \end{gathered}
dW = - F.dx
\begin{gathered}:\longmapsto \rm{dW = - q_{\circ}E .dx} \\ \end{gathered}
:⟼dW=−q
∘
E.dx
\begin{gathered}:\longmapsto\text{dW} = - \frac{\text{kqq}_{\circ}}{\text x {}^{2} } \\ \end{gathered}
:⟼dW=−
x
2
kqq
∘
⏩ Integrating Both Side ;
\begin{gathered}\text{W}_{\text P\rightarrow \infty } = - \int\limits^ \infty _\text r \text{kqq}_{\circ}( {\text x}^{ - 2} ) \ \text {dx}\\ \end{gathered}
W
P→∞
=−
r
∫
∞
kqq
∘
(x
−2
) dx
\begin{gathered} = - \text{kqq}_{\circ} {{\bigg[ - \frac{1}{\text x} \bigg]}_\text r^ \infty } \\ \end{gathered}
=−kqq
∘
[−
x
1
]
r
∞
\begin{gathered}\text{W}_{\text P \rightarrow \infty } = - \frac{\text{kqq}_{\circ}}{\text r} \\ \end{gathered}
W
P→∞
=−
r
kqq
∘
\large\red{\therefore \: \boxed{ \boxed{\text{W}_{\infty \rightarrow\text P } = \frac{\text{kqq}_{\circ}}{\text r} }}}∴
W
∞→P
=
r
kqq
∘
⏩ By Defination :
\begin{gathered}:\longmapsto \rm V_P=\frac{ W_{\infty \rightarrow P} }{q_{\circ}} \\\end{gathered}
:⟼V
P
=
q
∘
W
∞→P
\begin{gathered}:\longmapsto \rm V_P = \frac{{kqq}_{\circ}}{rq_{\circ}} \\ \end{gathered}
:⟼V
P
=
rq
∘
kqq
∘
\purple{ \large :\longmapsto \underline {\boxed{{\bf V_P = \frac{{kq}}{r}} }}}:⟼
V
P
=
r
kq
which is electric potential due to a Positive point charge at point P which is r distance away from Positive Charge.
Explanation:
Keep in mind is defined as to remain aware of something. An example of keep in mind is when you are reminded to think about your budget when you go shopping. verb.