Question

Three point charges are arranged along the x axis. Charge q 1 = -4.60 nC is located at x= 0.240 m and charge q 2 = 2.20 nC is at x= -0.320 m . A positive point charge q 3 is located at the origin.

a) What must the value of q3 be for the net force on this point charge to have magnitude 4.30 ?N.

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 = - 4.6 * 10^-9 C is at x1 = 0.24 m

q2 = 2.2 * 10^-9 C is at x2 = - 0.32 m

a)

the net force on q3 , F = K * q1 * q3 /x1^2 + K * q2 * q3 /x2^2

4.3 * 10^-6 = 9 * 10^9 * 10^-9 * q3 * (4.6/0.24^2 + 2.2/0.32^2 )

solving for q3

q3 = 4.71 * 10^-9 C = 4.71 nC

b)

let the net force is zero at x m

the net force at x ,F = K * q1 * q3 /( x1 - (x))^2 + K * q3 * q2 /( x2 + x )^2

as the net force is zero

0 = K * q1 * q3 /( x1 - (x))^2 + K * q3 * q2 /( x2 + x )^2

0 = 4.6 /( 0.24 - (x))^2 - 2.2 /( - 0.32 + x )^2

solving for x

x = - 0.5 m

the electric force is zero at x = - 0.5 m