Question

A proton moves with a speed of $5.0 \times 10^6 \, m/s^{-1}$ along the $x$-axis. It enters a region where there is a magnetic field of magnitude $2.0$ tesla directed at an angle of $30^{\circ}$ to the $x$-axis and lying in the $xy$ plane. The magnitude of the magnetic force on the proton is

• A. $0.8 \times 10^{-13} N $
• B. $1.6 \times 10^{-13} N $
• C. $18 \times 10^{-13} N $
• D. $8.0 \times 10^{-13} N $
• E. $16 \times 10^{-13} N $

Answer 1

Answer: (D)

Given,
The speed of proton,
$V=5.0 \times 10^{6} \,m / s$
Magnetic field, $B=2.0$ Tesla angle $\theta=30^{\circ}$
Charge on proton, $q=1.6 \times 10^{-19} C$
When the proton enters in magnitude field, it experiences Lorentz force
$ F =q( v \times B ) $
$|F| =q v B \sin \theta $
$ F =1.6 \times 10^{-19} \times 5 \times 10^{6} \times 2 \times \sin 30^{\circ} $
$=8.0 \times 10^{-13}\, N$