A proton (mass m,charge q) accelerated by a p | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) From the geometry of the path,the proton moves in a circular arc of radius $R$ within the magnetic field. From the figure,we have $\sin \alpha = \

Vedclass · Accepted Answer

$Bd \sqrt{\frac{q}{2mV}}$

Vedclass · Answer

(D) From the geometry of the path,the proton moves in a circular arc of radius $R$ within the magnetic field. From the figure,we have $\sin \alpha = \frac{d}{R}$.The magnetic force provides the necessary centripetal force,so $\frac{mv^2}{R} = qvB$,which gives the radius $R = \frac{mv}{qB}$.Substituting $R$ into the expression for $\sin \alpha$,we get $\sin \alpha = \frac{d}{mv/qB} = \frac{dqB}{mv}$.The kinetic energy gained by the proton is $\frac{1}{2}mv^2 = qV$,which implies $v = \sqrt{\frac{2qV}{m}}$.Substituting the value of $v$ into the expression for $\sin \alpha$:$\sin \alpha = \frac{dqB}{m \sqrt{\frac{2qV}{m}}} = \frac{dqB}{\sqrt{2mqV}} = Bd \sqrt{\frac{q^2}{2mqV}} = Bd \sqrt{\frac{q}{2mV}}$.Thus,the correct option is $D$.

Similar Questions

$A$ proton is projected with a velocity $10^7\, m/s$,at right angles to a uniform magnetic field of induction $100\, mT$. The time (in seconds) taken by the proton to traverse a $90^o$ arc is (given $m_p = 1.65 \times 10^{-27}\, kg$ and $q_p = 1.6 \times 10^{-19}\, C$).

An electron and a proton have equal kinetic energies. They enter a magnetic field perpendicularly. Then:

$A$ proton is moving perpendicular to a uniform magnetic field of $2.5 \ T$ with $2 \ MeV$ kinetic energy. The force on the proton is . . . . . . $N$. (Mass of proton $= 1.6 \times 10^{-27} \ kg$,charge of proton $= 1.6 \times 10^{-19} \ C$)

$A$ proton of velocity $\vec{v} = (3 \hat{i} + 2 \hat{j}) \text{ ms}^{-1}$ enters a magnetic field of induction $\vec{B} = (2 \hat{j} + 3 \hat{k}) \text{ T}$. The acceleration produced in the proton in $\text{ms}^{-2}$ is (Specific charge of proton $= 0.96 \times 10^8 \text{ C kg}^{-1}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module