A proton moves from south to north with a speed of \( 2 \times 10^{7}\,\mathrm{m\,s^{-1}} \). When a magnetic field is applied from west to east, the proton gets an acceleration of \( 10^{12}\,\mathrm{m\,s^{-2}} \). The mass of the proton is \( 1.6 \times 10^{-27}\,\mathrm{kg} \). The value of the magnetic field is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 5 \times 10^{-4}\,\mathrm{T} \)
The velocity (south to north) is perpendicular to the field (west to east), so the magnetic force has its full value \( F = evB \). By Newton's second law this force equals \( ma \).
\( \displaystyle evB = ma \;\Rightarrow\; B = \frac{ma}{ev} \)
\( m = 1.6\times10^{-27}\,\mathrm{kg} \)
\( a = 10^{12}\,\mathrm{m\,s^{-2}} \)
\( e = 1.6\times10^{-19}\,\mathrm{C} \)
\( v = 2\times10^{7}\,\mathrm{m\,s^{-1}} \)
\( \displaystyle B = \frac{1.6\times10^{-27} \times 10^{12}}{1.6\times10^{-19} \times 2\times10^{7}} = \frac{10^{-15}}{2\times10^{-12}} = 5\times10^{-4}\,\mathrm{T} \)