A conducting rod of length 2l is rotating wit | vedclass

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

Question

(D) The motional e.m.f. induced in a conductor moving in a magnetic field is given by $\varepsilon = \int (\vec{v} 	imes \vec{B}) \cdot d\vec{l}$.In

Vedclass · Accepted Answer

$Zero$

Vedclass · Answer

(D) The motional e.m.f. induced in a conductor moving in a magnetic field is given by $\varepsilon = \int (\vec{v} 	imes \vec{B}) \cdot d\vec{l}$.In this case, the magnetic field $\vec{B}$ is parallel to the axis of rotation.For any element $dr$ of the rod at a distance $r$ from the center $O$, the velocity vector $\vec{v}$ is perpendicular to the rod and lies in the plane of rotation.Since $\vec{B}$ is parallel to the axis of rotation, the vector $\vec{v} 	imes \vec{B}$ is directed along the rod.However, the motional e.m.f. is induced only if there is a component of the magnetic field perpendicular to the velocity and the length of the rod.Since $\vec{B}$ is parallel to the axis of rotation, the angle between $\vec{B}$ and the velocity vector $\vec{v}$ is $90^\circ$, but the magnetic field is perpendicular to the plane of rotation, meaning it is parallel to the axis of rotation. The force on the charge carriers $q(\vec{v} 	imes \vec{B})$ is directed perpendicular to both $\vec{v}$ and $\vec{B}$. Since $\vec{v}$ is in the horizontal plane and $\vec{B}$ is vertical, the force is radial. There is no force component along the length of the rod.Alternatively, the magnetic flux through the area swept by the rod is zero because the magnetic field lines are parallel to the axis of rotation and do not cut the area swept by the rod.Therefore, the induced e.m.f. between the two ends $A$ and $B$ is $Zero$.

$A$ conducting rod of length $2l$ is rotating with constant angular speed $\omega$ about its perpendicular bisector. $A$ uniform magnetic field $\overrightarrow{B}$ exists parallel to the axis of rotation. The e.m.f. induced between the two ends of the rod is

Similar Questions

Two identical thin bar magnets,each of length $l$ and pole strength $m$,are placed at a right angle to each other with the north pole of one touching the south pole of the other. The magnetic moment of the system is:

What is $X$ in the following reaction?
$2 CH_3COCH_3 \stackrel{Ba(OH)_2}{\longrightarrow} X$

The value of $\cos^{-1}\left(\cos\frac{5\pi}{3}\right) + \sin^{-1}\left(\cos\frac{5\pi}{3}\right)$ is

If $f: R \rightarrow R$ is defined by $f(x) = x - [x]$,where $[x]$ is the greatest integer not exceeding $x$,then the set of points of discontinuity of $f$ is

The least number among $\sqrt[3]{4}, \sqrt[4]{5}, \sqrt[4]{7}$ and $\sqrt[3]{8}$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module