In an experiment, electrons are accelerated, from rest, by applying, a voltage of $500 \,V.$ Calculate the radius of the path if a magnetic field $100\,mT$ is then applied. [Charge of the electron $= 1.6 \times 10^{-19}\,C$ Mass of the electron $= 9.1 \times 10^{-31}\,kg$ ]
JEE MAIN 2019, Medium
Download our app for free and get started
${{\text{k}}_{\text{e}}} = \frac{{{{\text{p}}^2}}}{{2{{\text{M}}_{\text{e}}}}} = 500\,{\text{e}} \ldots ({\text{i}})$
$\ \,{\text{R}} = \frac{{\text{p}}}{{{\text{eB}}}} = \frac{{1000{{\text{m}}_{\text{e}}}{\text{e}}}}{{{\text{eB}}}}$
$ = \frac{{1010 \times 9.1 \times {{10}^{ - 31}}}}{{1.6 \times {{10}^{ - 19}}}}$
$ = 100 \times 7.541 \times {10^{ - 6}}$
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
- 1Current $i$ is carried in a wire of length $L$. If the wire is turned into a circular coil, the maximum magnitude of torque in a given magnetic field $B$ will beView Solution
- 2Current $'i'$ is flowing in the rectangular loop placed in the $xyz$ plane as shown in the figure. Find the magnetic moment of the loopView Solution
- 3Assertion $(A):$ A wire bent into an irregular shape with the points $P$ and $Q$ fixed. If a current $I$ passed through the wire, then the area enclosed by the irregular portion of the wire increases.View Solution
Reason $(R):$ Opposite currents carrying wires repel each other.
- 4A current carrying long solenoid is placed on the ground with its axis vertical. A proton is falling along the axis of the solenoid with a velocity $v$. When the proton enters into the solenoid, it willView Solution
- 5The figure shows a circular loop of radius a with two long parallel wires (numbered $1$ and $2$) all in the plane of the paper. The distance of each wire from the centre of the loop is $d$. The loop and the wires are carrying the same current $I$. The current in the loop is in the counterclockwise direction if seen from above.$Image$View Solution
$1.$ When $d \approx$ a but wires are not touching the loop, it is found that the net magnetic filed on the axis of the loop is zero at a height $h$ above the loop. In that case
$(A)$ current in wire $1$ and wire $2$ is the direction $P Q$ and $R S$, respectively and $h \approx a$
$(B)$ current in wire $1$ and wire $2$ is the direction $PQ$ and $SR$, respectively and $h \approx a$
$(C)$ current in wire $1$ and wire $2$ is the direction $PQ$ and $SR$, respectively and $h \approx 1.2 a$
$(D)$ current in wire $1$ and wire $2$ is the direction $PQ$ and $RS$, resepectively and $h \approx 1.2 a$
$2.$ Consider $d \gg a$, and the loop is rotated about its diameter parallel to the wires by $30^{\circ}$ from the position shown in the figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new position will be (assume that the net field due to the wires is constant over the loop)
$(A)$ $\frac{\mu_0 I^2 a^2}{d}$ $(B)$ $\frac{\mu_0 I^2 a^2}{2 d}$ $(C)$ $\frac{\sqrt{3} \mu_0 I^2 a^2}{d}$ $(D)$ $\frac{\sqrt{3} \mu_0 I^2 a^2}{2 d}$
Give the answer question $1$ and $2.$
- 6When a charged particle moving with velocity $\vec V$ is subjected to a magnetic field of induction $\vec B$ , the force on it is non-zero. This implies theView Solution
- 7A uniform circular wire loop is connected to the terminals of a battery. The magnetic field induction at the centre due to $A B C$ portion of the wire will be (length of $A B C=l_1$, length of $A D C=l_2$ )View Solution
- 8Two very long, straight, parallel conductors $A$ and $B$ carry current of $5\,A$ and $10\,A$ respectively and are at a distance of $10\,cm$ from each other. The direction of current in two conductors is same. The force acting per unit length between two conductors is: $\left(\mu_0=4 \pi \times 10^{-7}\right.$ SI unit)View Solution
- 9A current $i$ ampere flows in a circular arc of wire whose radius is $R$, which subtend an angle $3\pi /2$ radian at its centre. The magnetic induction at the centre isView Solution
- 10A charge of $4.0 \mu \mathrm{C}$ is moving with a velocity of $4.0 \times 10^6 \mathrm{~ms}^{-1}$ along the positive $\mathrm{y}$-axis under a magnetic field $\vec{B}$ of strength $(2 \hat{k})\ T$. The force acting on the charge is $x \hat{i} N$. The value of $x$ is__________.View Solution