A charged particle moves in a uniform magnetic field B = (3î+2ĵ) T. Its acceleration is a = [4î-(x /2)ĵ] m·s⁻². Since the magnetic force is perpendicular to the magnetic field, find x.

Question

G1 Physics · Accepted Answer

For motion under a magnetic force, F = q(v×B), so the force, and hence the acceleration, is perpendicular to B. Therefore, a·B = 0. Given, a = 4î-(x ÷ 2)ĵ and B = 3î+2ĵ. Thus, a·B = 4×3 + [-x ÷ 2]×2 = 12-x. Set this equal to zero: 12-x = 0. Hence, x = 12.