A proton (mass= 1.67×10-27 kg, charge= 1.6×10-19 C) travelling with speed 1×106 m/s enters a region of space containing a uniform magnetic field of 1.2 T. What is the time t required for the proton to re-emerge into the field-free region? t =

The time required for the proton to re-emerge into the field-free region is 5.47 x 10⁻⁸ s

Explanation:

given;

mass of proton, m = 1.67 × 10⁻²⁷ kg

charge of proton, q = 1.6 × 10⁻¹⁹ C

speed of proton, v = 1 × 10⁶ m/s

uniform magnetic field, B = 1.2 T

Force on the proton due to uniform magnetic field = qvB

Force on the proton in the circular region = ma = mv²/r

The time required for the proton to re-emerge into the field-free region, is the same as the time required for the proton to return to its starting position. During this period, the proton has made one complete revolution.

v = 2πr/t

t = 2πr/v

where;

t is the required for the proton to re-emerge into the field-free region

r is the radius of the circular region

mv²/r = qvB

r = mv²/qvB

r = mv/qB

r = (1.67 × 10⁻²⁷ x 1 × 10⁶) / (1.6 × 10⁻¹⁹ x 1.2)

r = 8.698 x 10⁻³ m

t = 2πr/v

t = (2π x 8.698 x 10⁻³) / (1 × 10⁶)

t = 5.47 x 10⁻⁸ s

Therefore, the time required for the proton to re-emerge into the field-free region is 5.47 x 10⁻⁸ s