Question

Three point charges are arranged along the x axis. Charge q1 = -4.50 nC is located at x= 0.200 m and charge q2 = 2.20 nC is at x= -0.300 m . A positive point charge q3 is located at the origin. a. What must the value of q3 be for the net force on this point charge to have magnitude 3.00 μN. b. Where along the x axis can q3 be placed and the net force on it be zero, other than the trivial answers of x=+∞ and x=−∞?

Answer 1

here,

q1 = - 4.5 nC = - 4.5 * 10^-9 C is at x1 = 0.2 m

q2 = 2.2 nC = 2.2 * 10^-9 C is at x2 = - 0.3 m

a)

let the third charge be q3

Force , F = K * q1 * q3 /x1^2 + K * q2 * q3 /x2^2

3 * 10^-6 = 9 * 10^9 * q3 * 10^-9 * ( 4.5/0.2^2 + 2.2/0.3^2)

solving for q3

q3 = 2.43 * 10^-9 C = 2.43 nC

the third charge is 2.43 * 10^-9 C = 2.43 nC

b)

let the net force is zero at x

so, the net electric feild is also zero at point x

E = K * q1 /( x1 - x)^2 - K * q2 /( x - x2)^2

as the net electric feild is zero

0 = K * q1 /( x1 - x)^2 - K * q2 /( x - x2)^2

0 = 4.5 /( 0.2 - x)^2 - 2.2 /( x + 0.3)^2

solving for x

x = - 1.46 m

the net electric feild is zero at x = - 1.46 m