A straight rod of mass m and length L is susp | vedclass

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

Question

(C) $1$. Initially,the rod is in equilibrium under the force of gravity and the spring force. Let $k$ be the spring constant of each spring. The total

Vedclass · Accepted Answer

$\frac{mgR}{\varepsilon L}$; directed into the plane of the paper

Vedclass · Answer

(C) $1$. Initially,the rod is in equilibrium under the force of gravity and the spring force. Let $k$ be the spring constant of each spring. The total upward force from two springs is $2kx_0 = mg$,so $k = \frac{mg}{2x_0}$.$2$. When the magnetic field $B$ is switched on,a magnetic force $F_m = ILB$ acts on the rod. The current in the rod is $I = \frac{\varepsilon}{R}$.$3$. The springs extend by an additional distance $x_0$,meaning the total extension is $2x_0$. The new equilibrium condition is $2k(2x_0) = mg + F_m$.$4$. Substituting $2kx_0 = mg$ into the equation: $2(2kx_0) = 2mg = mg + F_m$,which implies $F_m = mg$.$5$. Since $F_m = ILB = \frac{\varepsilon}{R}LB = mg$,we solve for $B$: $B = \frac{mgR}{\varepsilon L}$.$6$. To increase the extension,the magnetic force must act downwards. By Fleming's Left-Hand Rule,with current flowing in a specific direction,the magnetic field must be directed into the plane of the paper to produce a downward force.

Similar Questions

$A$ straight current-carrying conductor is placed such that the current flows out of the plane of the paper. The conductor is placed between the poles of two magnets,as shown in the figure. The conductor will experience a force in the direction towards:

Three long,straight parallel wires carrying current are arranged as shown in the figure. The force experienced by a $25\, cm$ length of wire $C$ is

The force acting on a current-carrying wire joining two fixed points $A$ and $B$ in a uniform magnetic field is:

For the circuit shown in the figure,the direction and magnitude of the force on the segment $PQR$ is:

$A$ straight wire of mass $200 \;g$ and length $1.5 \;m$ carries a current of $2 \;A$. It is suspended in mid-air by a uniform horizontal magnetic field $B$ (Figure). What is the magnitude of the magnetic field (in $T$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module