An electricity and magnetism problem by Ronak Agarwal

Electricity and Magnetism Level 3

Find the force on a uniformly charged hollow sphere of radius 1 m 1m and surface charge density σ = 0.5 μ C / m 2 \sigma = 0.5\quad \mu C/{ m }^{ 2 } by a point sized particle of charge q = 10 − 3 q={ 10 }^{ -3 } columbs placed at a distance 5 m 5 m from the centre of the sphere

Take ε 0 { \varepsilon }_{ 0 } = 8.85 × 10 − 12 C 2 / N M 2 = 8.85\times { 10 }^{ -12 }\quad { C }^{ 2 }/N{ M }^{ 2 }


The answer is 2.259.

Ronak Agarwal by Ronak Agarwal , 23, India

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3 solutions

Using Newton's Third Law,

F f o r c e o n s p h e r e d u e t o c h a r g e = F f o r c e o n c h a r g e d u e t o s p h e r e = F F_{force on sphere due to charge} = F_{force on charge due to sphere} = F

Electric Field at a distance of 5 m e t e r s 5 meters from the hollow sphere is given by

E = 1 4 π ϵ 0 × Q 5 2 E = \frac{1}{4\pi\epsilon_{0}} \times \frac{Q}{5^{2}}

where Q = σ × 4 π Q = \sigma \times {4\pi}

Now,

F = q × E F = q\times{E} where q = 1 0 − 3 C q = 10^{-3} C

Substituting given values,

F = 2.259 N \boxed{F = 2.259 N}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Ronak Agarwal
Jun 27, 2014

The force on the sphere by the charged particle is equal to the force of the charged particle by the sphere which can be calculated very easily

1 Helpful 0 Interesting 0 Brilliant 0 Confused
God Knows
Oct 17, 2014

USE DIRECTLY FORMULA

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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