Proton with kinetic energy of $1\;MeV$ moves from south to north. It gets an acceleration of $10^{12}\; \mathrm{m} / \mathrm{s}^{2}$ by an applied magnetic field (west to east). The value of magnetic field :.......$mT$ (Rest mass of proton is $1.6 \times 10^{-27} \;\mathrm{kg}$ )
JEE MAIN 2020, Medium
Download our app for free and get started
$\mathrm{a}=\frac{\mathrm{qvB}}{\mathrm{m}}$
$\mathrm{B}=\frac{\mathrm{ma}}{\mathrm{qv}}=\frac{\mathrm{ma} \sqrt{\mathrm{m}}}{\sqrt{2 \mathrm{k}}}$
$=\frac{\mathrm{m}^{3 / 2} \mathrm{a}}{\mathrm{e} \sqrt{2 \mathrm{k}}}=\frac{\left(1.6 \times 10^{-27}\right)^{3 / 2} \times 10^{12}}{1.6 \times 10^{-19} \sqrt{2 \times 1 \times 10^{6} \times 1.6 \times 10^{-19}}}$
$=0.71 \mathrm{mT}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two very thin metallic wires placed along $X$ and $Y$-axis carry equal currents as shown here. $AB$ and $CD$ are lines at $45^\circ $ with the axes with origin of axes at $O$. The magnetic field will be zero on the lineView Solution
- 2View SolutionA stream of charged particles enter into a region with crossed electric and magnetic fields as shown in the figure below. On the other side is a screen with a hole that is right on the original path of the particles. Then,
- 3In the previous question, if the current is $i$ and the magnetic field at $D$ has magnitude $B$,View Solution
- 4A conductor in the form of a right angle $ABC$ with $AB = 3\, cm$ and $BC = 4\, cm$ carries a current of $10\, A$. There is a uniform magnetic field of $5\, T$ perpendicular to the plane of the conductor. The force on the conductor will be......$N$View Solution
- 5Two thick wires and two thin wires, all of the same materials and same length form a square in the three different ways $P$, $Q$ and $R$ as shown in fig with current connection shown, the magnetic field at the centre of the square is zero in casesView Solution
- 6As shown in the figure, the uniform magnetic field between the two identical plates is $B$. There is a hole in plate. If through this hole a particle of charge $q$, mass $m$ and energy $E$ enters this magnetic field, then the particle will not collide with the upper plate providedView Solution
- 7A cylindrical conductor of radius $'R'$ carries a current $'i'$. The value of magnetic field at a point which is $R/4$ distance inside from the surface is $10\,T$. Find the value of magnetic field at point which is $4R$ distance outside from the surfaceView Solution
- 8A wire carrying current $I$ and other carrying $2I$ in the same direction produces a magnetic field $B$ at the mid point. What will be the field when $2I$ wire is switched offView Solution
- 9A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbitals in a plane due to magnetic field perpendicular to the plane. Let $r_p, r_e$ and $r_{He}$ be their respective radii, thenView Solution
- 10A solenoid of $N$ turn, $'l'$ length and $'r'$ radius of cross - section. If current $i$ flow in solenoid then magnetic field at axial mid point will be (where $l\, \simeq \,\,r$ )View Solution