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If a rod is of length l then at which height on the centre of the rod will the electric field the maximum?

If a rod is of length l then at which height on the centre of the rod will the electric field the maximum?

Grade:12

1 Answers

Ashish Kumar
106 Points
4 years ago
The maximum electric field will be at length l/2√2. To get the answer you will have to perform integration.I am explainting it how you’ll do it because that’s the only difficult part. First take a length x from the centre of rod then take dx after x. Now on dx calculate the charge.For these types of questions generally the charge per unit length is given so i am assuming it to be Q. So charge on dx becomes Qdx.Now let the height of the point on the centre be h.Now the height from dx becomes h/cos(theta) where theta is angle from x axis. Now apply formula
so E.F = kQdx/{h/cos(theta) }2.Now put the value of cos theta in temrs of h and l and then integrate it in limit -l/2 to l/2 then differentiate it again to get the maxima and minima and then its just class eleventh integral solve.
Hope it will help..!

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