Question

Point charges of 23.0 µC and 35.0 µC are placed 0.550 m apart.

At what point (in m) along the line between them is the electric field zero?

What (in N/C) is the electric field halfway between them?

Answer 1

Let P be the point in between 23 C charge and 35 C charge so that resultant electric field is zero at P.

P is at a distance d from 23 C

Then we have , [ 23 10-6 ] / [ (4o ) d2 ] = [ 35 10-6 ] / [ (4o ) (0.550-d)2 ]

By simplifying above equation, we get, 23 ( 0.550 - d)2 = 35 d2

By simplifying above equation, we get , d2 + 2.111 d - 0.581 = 0

above quadratic equation has acceptable solution as , d = 0.246 m

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At Halfway , electric field E1 due to 23 C is given by

electric field E1 due to 35 C is given by

Since E2 > E1 , Resultant electric field ER is given by

( -ve direction is given , because the field is towards 23 C charge , i.e., towards left )