A proton moving in the positive x direction with a speed of 8.7 105 m/s experiences zero magnetic force. When it moves in the positive y direction it experiences a force of 2.1 10-13 N that points in the positive z direction. Determine the magnitude and direction of the magnetic field.

Explanation:

The force on a moving charge in a magnetic field acts in a direction perpendicular to the plane containing the magnetic field and the velocity of propagation of charge.

If charge flows in the direction of magnetic field , or opposite to magnetic field ,no force will act on the charge . Here no force is acting on the moving charge , therefore magnetic field must be along or against the direction of velocity of proton. Hence , magnetic field must be along or againt  positive x direction.

b = B i or - Bi

if the proton moves along positive y direction , its velocity can be represented by the formula

v = 8.7 x 10⁵ j

Direction of force positive z direction so

F = 2.1 x 10⁻¹³ k

F = q ( v x b )

2.1 x 10⁻¹³ k = 1.6 x 10⁻¹⁹ x (8.7 x 10⁵ j x  B i )

2.1 x 10⁻¹³ k  = - 13.92  x 10⁻¹⁴k B

It is not matching so B is not along positive x direction . If it is in - x direction

b = - Bi

F = q ( v x b )

2.1 x 10⁻¹³ k = 1.6 x 10⁻¹⁹ x (8.7 x 10⁵ j x  - B i )

2.1 x 10⁻¹³ k  =  13.92  x 10⁻¹⁴k B

B = 1.5 T in negative x direction

true tan speed = ang vel x radius