Question

Asked May 3, 2019

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Step 1

(a) Due to the symmetry, the *x*-component of the electric field as a point lying on the perpendicular bisector of the rod is zero. The electric field due to the charge element on left portion of the rod cancels with electric field due to the charge element on right portion. That is E* _{x}* = 0.

b) The electric field at a point on the perpendicular bisector at distance *R *from the rod is shown in the following diagram. The electric field at P due to a small line element *dx* can be calculated using Coulombs law as follows.

Step 2

There is symmetrical line element at exactly opposite side of the line charge. The electric field due to that line element is same as calculated above. The sum of *y *component of electric field due to both line element *dx* is given below.

Step 3

Integrate above equation within a limit of L/2 to 0 to get *x...*

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