Question

A charge is placed at x = 0 meters and another charge of 5 micro-coulombs is placed at x = +4.4 m (both on the x axis). The total electric field produced by these two charges is zero at x = +2.1 meters. Then the charge at x = 0 m, switches sign but its magnitude is not changed. Where on the x axis (x = ____ m), is the total electric field equal to zero now? Answer in meters.

Answer 1

Net field is zero means force due to both charges at x=2.1 are same and opposite.let unknown charge is q1 and q2 is 5 micro-coulombs. so, equating the fields, kq1/2.1^2= kq2/2.3^2 { since 4.4-2.1= 2.3 }

So, q1= 2.1^2 * q2 / 2.3^2 = 4.17 micro-coulombs which is +ve

Now, at x=0 and 4.4 there are -ve and +ve charge. So, net field shall be zero at a point with x<0 as it should be nearer to q1 than q2.

So, kq1/x^2= kq2/(4.4+x)^2

Or, 4.17/5= x^2/ (4.4+x)^2

Or, (1.199)^1/2= (4.4+x)/x

So, 4.4/x + 1 = 1.095

So, x= 4.4/0.095= 46.31m

As mentioned above this point is in -ve x axis so , on the x axis at (x = -46.31 m), the total electric field  is equal to zero now.

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