A thin insulating rod of length L carries a uniformly distributed charge Q. Find the electric field strength at a point along its axis at a distance ‘a’ from one end.

Solution

Let us consider an infinitesimal element of length dx at a distance x from the point P.

The charge on this element is dq = λdx,
where, $λ = \frac{Q}{L}$ is the linear charge density.

The magnitude of the electric field at P due to this element is
$dE = \frac{1}{4 {πε}_{0}} \frac{dq}{x^{2}} = \frac{1}{4 {πε}_{0}} \frac{(λdx)}{x^{2}}$

and its direction is to the right since X is positive.
The total electric field strength E is given by
$E = \frac{1}{4 {πε}_{0}} λ \int_{a}^{a + L} \frac{dx}{x^{2}}$

$= \frac{λ}{4 {πε}_{0}} {[- \frac{1}{x}]}_{a}^{a + L} = \frac{λ}{4 {πε}_{0}} [\frac{1}{a} - \frac{1}{a + L}] = \frac{Q}{(4 {πε}_{0}) a (a + L)} (∴ Q = λL)$

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?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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Electric Charges And Fields

A thin insulating rod of length L carries a uniformly distributed charge Q. Find the electric field strength at a point along its axis at a distance ‘a’ from one end.

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?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

A thin insulating rod of length L carries a uniformly distributed charge Q. Find the electric field strength at a point along its axis at a distance ‘a’ from one end.

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?

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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?