Two positive charges `q_1 and q_2` are moving with velocities `v_1 and v_2` when they are at points A and B, respectively, as shown in Fig. The magnetic force experienced by charge `q_1 ` due to the other charge `q_2` is

Options

A. `(mu_0q_1q_2v_1v_2)/(8sqrt2pia^2)`
B. `(mu_0q_1q_2v_1v_2)/(4sqrt2pia^2)`
C. `(mu_0q_1q_2v_1v_2)/(2sqrt2pia^2)`
D. `(mu_0q_1q_2v_1v_2)/(sqrt2pia^2)`

Answer

A

Explanation

(a) Magnetic field at A due to `q_2`: `vecB_2=(mu_0)/(4pi) (q_2v_2rsin 45^@)/(r^3)hatk` where `r=sqrt2a`
`implies vecB_2=(mu_0)/(4pi) (q_2v_2)/(2sqrt2a^2) hatk`
Force on `q_1 : vecF=q_1vecv_1xxvecB_2=(mu_0)/(4pi) (q_1q_2v_1v_2)/(2sqrt2a^2)(-hatj)`