Two point charges, 6.0 µC and -2.0 µC, are placed 4.6 cm apart on the x axis, su

Question

Two point charges, 6.0 µC and -2.0 µC, are placed 4.6 cm apart on the x axis, such that the -2.0 µC charge is at x = 0 and the 6.0 µC charge is at x = 4.6 cm.

(a) At what point(s) along the x axis is the electric field zero? (If there is no point where E = 0 in a region, enter "0" in that box.)

(b) At what point(s) along the x axis is the potential zero? Let V = 0 at r = . (If there is no point where V = 0 in a region, enter "0" in that box.)

Explanation / Answer

a)
let

q1 = -2 micro C

q2 = 6 micro C

here, |q1| < |q2|, so the point where net electric filed is zero is close to q1 and it is left to q1.

llet x is the distance from q1 where Enet is zero.

Apply, E1 = E2

k*q1/x^2 + k*q2/(d+x)^2

q1/x^2 = q2/(d+x)^2

(d+x)^2/x^2 = q2/q1

(d+x)/x = sqrt(q2/q1)

(4.6+x)/x = sqrt(6/2)

4.6+x = 1.732*x

4.6 = 0.732*x

==> x = 4.6/0.732

= 6.28 cm

so, at x = -6.28 cm , Enet = 0 <<<<<<<<<<<<<<<---------Answer

b) The point where Vnet is zero is close to q1 and it right to q1.

let x is the distance x from q1 where vnet = 0

Apply, V1 = V2

k*q1/x = k*q2/(d-x)

q1/x = q2/(d-x)

2/x = 6/(d-x)

(d-x)/x = 6/2

d-x = 3*x

d = 4*x

==> x = d/4

= 6/4

= 1.5 cm

so, at x = 1.5 cm , Vnet = 0 <<<<<<<<<<<<<<<---------Answer

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