The figure shows a region of length $'l'$ with a uniform magnetic field of $0.3\, T$ in it and a proton entering the region with velocity $4 \times 10^{5}\, ms ^{-1}$ making an angle $60^{\circ}$ with the field. If the proton completes $10$ revolution by the time it cross the region shown, $l$ is close to....... $m$
(mass of proton $=1.67 \times 10^{-27} \,kg ,$ charge of the proton $\left.=1.6 \times 10^{-19}\, C \right)$
JEE MAIN 2020, Diffcult
Download our app for free and get started
Sol. $\quad T =\frac{2 \pi m }{ qB }$
total time $t=10 T$
Kinematics
$\ell=\frac{ V }{2} t$
$\ell=\frac{V}{2} 10 \times \frac{2 \pi m}{q B}$
$=4 \times 10^{5} \times 10 \times \frac{3.14 \times 1.67 \times 1 0^{-27}}{1.6 \times 10^{-19} \times 0.3}$
$=0.439$
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
- 1A cylindrical cavity of diameter a exists inside a cylinder of diameter $2$a shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density $J$ flows along the length. If the magnitude of the magnetic field at the point $P$ is given by $\frac{N}{12} \mu_0$ aJ, then the value of $N$ is :View Solution
- 2The resistance of $1\, A$ ammeter is $0.018\,\Omega $. To convert it into $10\, A$ ammeter, the shunt resistance required will beView Solution
- 3As shown in the figure, a metallic rod of linear density $0.45\,kg\,m ^{-1}$ is lying horizontally on a smooth incline plane which makes an angle of $45^{\circ}$ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when $0.15\,T$ magnetic field is acting on it in the vertical upward direction, will be $....A$ $\left\{\right.$ Use $\left.g=10 m / s ^{2}\right\}$View Solution
- 4The electrostatic force $\left(\vec{F}_1\right)$ and magnetic force $\left(\vec{F}_2\right)$ acting on a charge $q$ moving with velocity $v$ can be written :View Solution
- 5Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field $B$ = $B_0\hat{k}$View Solution
- 6An ammeter gives full scale deflection when current of $1.0\, A$ is passed in it. To convert it into $10\, A$ range ammeter, the ratio of its resistance and the shunt resistance will beView Solution
- 7A uniform magnetic field of $0.3\; T$ is established along the positive $Z$ -direction. A rectangular loop in $XY$ plane of sides $10 \;cm$ and $5 \;cm$ carries a current of $I =12\; A$ as shown. The torque on the loop isView Solution
- 8A electron $(q = 1.6 \times 10^{-19}\, C)$ is moving at right angle to the uniform magnetic field $3.534 \times 10^{-5}\, T$. The time taken by the electron to complete a circular orbit is......$µs$View Solution
- 9A circular coil of wire carries a current. $PQ$ is a part of a very long wire carrying a current and passing close to the circular coil. If the directions of currents are those shown in figure, what is the direction of force acting on $PQ$ ?View Solution
- 10The resistance of a galvanometer is $90\, ohms$. If only $10$ percent of the main current may flow through the galvanometer, in which way and of what value, a resistor is to be usedView Solution