A uniform line charge of linear charge density λ coulombs per metre exists along the x-axis from x = – a to x = + a. Find the electric field intensity E at a point P at a distance r along the perpendicular bisector.

Solution

In all the problems, which involve distribution of charge, we choose an element of charge dq to find the element of the field dE produced at the given location. Then we sum all such dEs to find the total field E at that location.
We must note the symmetry of the situation. For each element dq located at positive x-axis. There is a similar dq located at the same negative value of x. The dE_x produced by one dq is cancelled by the dE_x in the opposite direction due to the other dq. Hence, all the dE_xcomponents add to zero.
So, we need to sum only the dE_y components, a scalar sum since they all point in the same direction.
The element charge is dq = λ dx

The integral on the right hand side can be evaluated by substituting x = $r \tan α$ and dx = r sec² $α$ . $dα$

[ $\sin α = \frac{x}{\sqrt{x^{2} + r^{2}}}$ ]

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Electric Charges And Fields

A uniform line charge of linear charge density λ coulombs per metre exists along the x-axis from x = – a to x = + a. Find the electric field intensity E at a point P at a distance r along the perpendicular bisector.

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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For Daily Free Study Material Join wiredfaculty

Electric Charges And Fields

A uniform line charge of linear charge density λ coulombs per metre exists along the x-axis from x = – a to x = + a. Find the electric field intensity E at a point P at a distance r along the perpendicular bisector.

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?