Question

Point charge q1q1q_1 = −7.00×10⁻⁶ CC is on the xx-axis at xxx_1 = -0.200 mm . Point charge q2q2 is on the xx-axis at xx = +0.5 mm . Point charge q3q3 = +3.00××10−6−6 CC is at the origin.

What is q2q2 (magnitude and sign) if the net force on q3q3 is 6.00 NN in the +x+x-direction

What is q2q2 (magnitude and sign) if the net force on q3q3 is 6.00 NN in the −x−x-direction;

Answer 1

The charge q₁ attracts q₃ with a force of F₁₃ = kq₁q₃ / r²₁₃ = 9 x 10⁹ x 7 x 10^-6 x 3 x 10^-6 / 0.2² = 4.725 N in the negative x direction.

Therefore, if the net force is in the +ve x direction, then the charge 2 will be negative because to produce a net force of 6 N in the +ve x direction it has to be negative to attract the charge 3 with a greater force than charge 1.If the charge 2 is positive total net force will be produced in the -ve x direction which is not the case in (i).

Similarly, if the net force is in the -ve x direction, then the charge 2 will be positive because to produce a net force of 6 N in the -ve x direction it has to be positive to repel the charge 3. The charge 1 attracts charge 3 with a force of 4.725 N, so for a net force of 6 N in the negative direction, the charge 2 will be positive. If the charge is negative, then the net force can never be 6 N in the negative x direction as given in (ii).

Let the magnitude of charge be q_2.(Ignore the sign during calculation, just remember the direction of force.)