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Electric Charges And Fields

Question

Show that for a uniformly charged hollow sphere, the electric field has a maximum value at the surface of the sphere.

Solution

Consider a thin spherical shell of radius 'R' with centre O. Let, a charge +q be distributed uniformly on the surface of the shell.
According to gaussian theorem,

$\oint E . d s = \oint \overset{⇀}{E} . \overset{⏜}{n} . d s = \frac{q}{ε_{o}}$
Surface area of the sphere = 4 $π$ r²

$∴ E . 4 {πr}^{2} = \frac{q}{ε_{o}}$

Now, at a point on the surface area of the shell
Let, $σ$ be the surface charge density on the shell,
then,
q = 4 $π$ R² . $σ$

$\Rightarrow$ $E = \frac{4 {πR}^{2} σ}{4 {πε}_{o} R^{2}} = \frac{σ}{ε_{\circ}}$

Therefore,
$E = \frac{σ}{ε_{o}}$
which is the required electric field at the surface of the shell.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

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Electric Charges And Fields

Show that for a uniformly charged hollow sphere, the electric field has a maximum value at the surface of the sphere.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

Show that for a uniformly charged hollow sphere, the electric field has a maximum value at the surface of the sphere.

Some More Questions From Electric Charges and Fields Chapter

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?b) Explain why two field lines never cross each other at any point?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
b) Explain why two field lines never cross each other at any point?