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 small element $dx$ of a rod moving with velocity $v$ in a magnetic field $B$ is given by $de = B v dx$.Since th

Vedclass · Accepted Answer

Zero

Vedclass · Answer

(D) The motional $e.m.f.$ induced in a small element $dx$ of a rod moving with velocity $v$ in a magnetic field $B$ is given by $de = B v dx$.Since the rod is rotating with angular speed $\omega$ about its perpendicular bisector,the velocity of an element at distance $x$ from the center is $v = \omega x$.Thus,$de = B (\omega x) dx$.The magnetic field $\vec B$ is parallel to the axis of rotation. The velocity vector $\vec v$ of any point on the rod is perpendicular to the radius vector (in the plane of rotation),and the magnetic field $\vec B$ is perpendicular to this plane of rotation.However,the motional $e.m.f.$ is induced only when the velocity vector $\vec v$ has a component perpendicular to the magnetic field $\vec B$. Here,$\vec v$ is always in the plane of rotation,and $\vec B$ is perpendicular to this plane. Thus,$\vec v \perp \vec B$ is satisfied for all points.But for a rod rotating about its center,the induced $e.m.f.$ between the center and one end is $\int_0^l B \omega x dx = \frac{1}{2} B \omega l^2$.Since the rod is symmetric about the center,the potential at both ends is the same relative to the center. Therefore,the potential difference between the two ends is $V_{end1} - V_{end2} = (V_{center} + \frac{1}{2} B \omega l^2) - (V_{center} + \frac{1}{2} B \omega l^2) = 0$.Hence,the induced $e.m.f.$ between the two ends is zero.

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

Similar Questions

The formula of sodium nitroprusside is .........

$A$ coordination complex contains $Co^{3+}$,$Cl^{-}$,and $NH_3$. When dissolved in water,one mole of this complex gives a total of $3$ moles of ions. The complex is

If $\cos ^{-1}\left(\frac{5}{13}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\cos ^{-1} x$,then $x$ is equal to

If $a \cdot \hat{i} = a \cdot (\hat{i} + \hat{j}) = a \cdot (\hat{i} + \hat{j} + \hat{k})$, then $a$ is equal to

$A$ particle is projected with a velocity $v$ such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where $g$ is acceleration due to gravity)

Vedclass Test Series

Exam Paper Generator

Online Exam Module