A pair of point charges, q = 4.7 ?C and q\' = -2.7 ?C, are moving as shown in th

Question

A pair of point charges, q = 4.7 ?C and q' = -2.7 ?C, are moving as shown in the figure above with speeds v = 8.1 x 104 m/s and v' = 9.6 x 104 m/s. The charges are at the locations shown in the figure.

A.) What is the magnitude of the magnetic field at the origin? (include units with answer)

B.) What is the magnitude of the magnetic force that q' exerts on q? (include units with answer)

C.) What is the direction of the magnetic force that q' exerts on q? (CCW from +x direction)
(include units with answer)

I will rate, please include answer and work so i can understand. Thanks!

Explanation / Answer

Solution: (A) According to Biot-Savart?s law: B = (?0/4?) q(v x r)/r2 where B is the magnetic field vector, v is the velocity vector and r is the unit position vector.

So, for the +q charge, B = 0.19 T in the ?into the page? direction (using simple v x r cross product).

Similarly, for the ?q charge, B? = 0.24 T again in the ?into the page? direction (due to negative charge).

So the total magnetic field at the origin becomes 0.43 T into the page direction.

(B) Magnetic force exerted on a charge due to a current carrying element is F = iL x B

So, considering q to be at rest, F = 62208 N; a massive force as the amount of charge is colossal moving with high velocity.

(C) Magnetic force will act along negative x-axis. As i is along ?ve y-axis and B is into the page, a simple cross product using screw rule will yield the answer.

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