Question

Two point charges, q₁= +2 nC and q₂= -18 nC, are located on the x-axis at x= 0 and x=4 m. What is the distance of ZERO electric field from the positive charge?

Answer 1

Lets divide the no line into 3 parts.

(A) x<0, (B.)0<x<4 (C.) x>4

Now for part A, electric field due to q1 is in -x direction and electric field due to q2 is in +x direction So , we can have zero electric field in this reason.

Now for part B, electric field due to q1 is in +x direction and electric field due to q2 is in +x direction So , we can not have zero electric field in this reason.

Now for part A, electric field due to q1 is in +x direction and electric field due to q2 is in -x direction So , we can have zero electric field in this reason.

Now when we carefully observe we conclude that since magnitude of q1<q2 so the zero electric field point must be closer to q1. So Part C cant have zero electric field.

Thus we are left with one part i.e, A.

Now lets suppose distance of zero electric field point from q1 be x (in -x direction)

then its distance from q1=4+x

Now for the two to cancel the magnitudes of electric fields must be same

i.e, k.q1/x²=k.q1/(4+x)²

i.e, k.2/x²=k.18/(4+x)² (Taking magnitudes only)

i.e, 2(4+x)² =18x²

i.e, 2x²+16x+32=18x²

i.e, 16x²-16x-32=0

i.e, x²-x-2=0

i.e, x²-2x+x-2=0

i.e, x(x-2)+1(x-2)=0

i.e, (x-2)(x+1)=0

so, x=2 or x=-1.

Ignoring negative sign because that would mean point would be in 2nd part.

So, the required point is 2 m in the -x direction from q1. i.e, at x=-2.