Question

A proton travelling at 35 degree to an external magnetic field of magnitude 0.026 T experiences a force of magnitude 5.5x10^-17 N. Hint: Use formula F = qvBsineθ (a) Calculate the speed of the proton. (b) Calculate the kinetic energy of the proton in both joules (J) and electron volts (eV).

Answer 1

a) 2.3 x 10⁴ m/s

b) 4.42 x 10⁻¹⁹ J or 2.8 eV

Step-by-step explanation:

θ = Angle between the direction of motion of proton and magnetic field = 35

B = magnitude of magnetic field = 0.026 T

F = magnitude of magnetic force =5.5 x 10⁻¹⁷ N

q = magnitude of charge on proton = 1.6 x 10⁻¹⁹ C

v = speed of proton

magnetic force on proton is given as

F = q v B Sinθ

5.5 x 10⁻¹⁷ = (1.6 x 10⁻¹⁹) (0.026) Sin35 v

v = 2.3 x 10⁴ m/s

b)

m = mass of the proton = 1.67 x 10⁻²⁷ kg

Kinetic energy of proton is given as

KE = (0.5) m v²

KE = (0.5) (1.67 x 10⁻²⁷) (2.3 x 10⁴)²

KE = 4.42 x 10⁻¹⁹ J

we also know that, 1 eV = 1.6 x 10⁻¹⁹ J

KE =
`(4.42* 10^(-19))/(1.6* 10^(-19))`

KE = 2.8 eV