A conducting bar of mass m and length l moves | vedclass

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

Question

(C) As the bar moves to the right,the area of the loop increases,which increases the magnetic flux through the loop. According to Lenz's law,the induc

Vedclass · Accepted Answer

distance the bar travels before it comes to a complete stop is proportional to $R$

Vedclass · Answer

(C) As the bar moves to the right,the area of the loop increases,which increases the magnetic flux through the loop. According to Lenz's law,the induced current will flow in a direction to oppose this increase in flux. Thus,the current flows counter-clockwise.The magnetic force on the bar is $F = IlB = (\frac{Blv}{R})lB = \frac{B^2l^2v}{R}$. This force acts to the left,opposing the motion.Using Newton's second law,$ma = -F = -\frac{B^2l^2v}{R}$.Thus,$m \frac{dv}{dt} = -\frac{B^2l^2v}{R}$. This shows that the velocity decreases exponentially with time,not linearly.To find the distance $x$,we use $v \frac{dv}{dx} = -\frac{B^2l^2v}{Rm}$.Integrating $dv = -\frac{B^2l^2}{Rm} dx$ from $v_0$ to $0$ and $0$ to $x_{max}$:$v_0 = \frac{B^2l^2}{Rm} x_{max} \Rightarrow x_{max} = \frac{m v_0 R}{B^2l^2}$.Therefore,the distance traveled is proportional to $R$.

$A$ conducting bar of mass $m$ and length $l$ moves on two frictionless parallel rails in the presence of a constant uniform magnetic field of magnitude $B$ directed into the page as shown in the figure. The bar is given an initial velocity $v_{0}$ towards the right at $t=0$. Then,the:

Similar Questions

$A$ wire of length $1 \, m$ is moving at a speed of $2 \, m/s$ perpendicular to a homogeneous magnetic field of $0.5 \, T$. The ends of the wire are joined to a resistance of $6 \, \Omega$. The rate at which work is being done to keep the wire moving at that speed is:

$A$ metal rod of length $2 \, m$ is rotating with an angular velocity of $100 \, rad/s$ in a plane perpendicular to a uniform magnetic field of $0.3 \, T$. The potential difference between the ends of the rod is.......$V$

Vedclass Test Series

Exam Paper Generator

Online Exam Module