Math, asked by ananditamahani1678, 4 days ago

If ||V|| =1, Then V is called

Answers

Answered by amitvijayshree2009
0

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.

Step-by-step explanation:

same

Answered by poonamchavhan000
0

Answer:

lf ||v|| =1 then v is called

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