Physics

Electrostatic Potential and Capacitance

Electric potential

Calculate the potential due to a thin charged rod of length L

Question

Medium

Solving time: 3 mins

Calculate the potential due to a thin charged rod of length $L$ at the point along and perpendicular to its length.

Name: Video answer for Calculate the potential due to a thin charged rod of length L at the point along and perpendicular to its length.
Uploaded: 2022-11-13T16:27:35.000Z
Duration: 14 min
Description: Calculate the potential due to a thin charged rod of length L at the point along and perpendicular to its length.

Views: 5,371 students

Updated on: Nov 13, 2022

Book:

Electrostatics (Disha)

Text solutionVerified

Suppose a thin rod has a uniform linear charge density

λ

. To find potential at point

P

, let us divide the rod into a series of small elements of thickness

d x

each. Consider such an element at a distance

x

from

O

. The charge on the element

d q = λ d x

The potential due to the element at point

P

d V = (\frac{1}{4 π \in _{0}}) \frac{λ d x}{r}

The potential due to the entire rod.

V = (\frac{1}{4 π ϵ _{0}})^{(L + a)} \int_{a}^{λ d x} = (\frac{1}{4 π ϵ _{0}}) \int_{a}^{(L + a)} \frac{λ d x}{( b ^{2} + x ^{2} ) ^{1/2}} = (\frac{λ}{4 π ϵ _{0}}) [ln {x + b^{2} + x^{2}}]_{a}^{L + a}] = (\frac{λ}{4 π ϵ _{0}}) ln [\frac{( L + a ) + b ^{2} + ( L + a ) ^{2}}{a + b ^{2} + a ^{2}}]

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Question Text	Calculate the potential due to a thin charged rod of length $L$ at the point along and perpendicular to its length.
Updated On	Nov 13, 2022
Topic	Electrostatic Potential and Capacitance
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 1
Upvotes	221
Avg. Video Duration	14 min

Calculate the potential due to a thin charged rod of length $L$ at the point along and perpendicular to its length.

Text solutionVerified

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