When a J-shaped conducting rod is rotating in | vedclass

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

Question

(C) The induced electromotive force $(emf)$ across a rotating conducting rod in a uniform magnetic field is given by the formula $e = \frac{1}{2} B \o

Vedclass · Accepted Answer

$\frac{1}{2}B\omega(L^2 + l^2)$

Vedclass · Answer

(C) The induced electromotive force $(emf)$ across a rotating conducting rod in a uniform magnetic field is given by the formula $e = \frac{1}{2} B \omega r^2$,where $r$ is the perpendicular distance from the axis of rotation to the end of the rod.In this case,the rod is $J$-shaped,but the induced $emf$ depends only on the displacement vector between the two endpoints of the rod relative to the axis of rotation.The effective distance $r$ from the pivot point $P$ to the other end $Q$ is the straight-line distance between them. Based on the geometry of the rod,this distance is $r = \sqrt{l^2 + L^2}$.Substituting this into the formula,we get:$e = \frac{1}{2} B \omega (\sqrt{l^2 + L^2})^2$Simplifying the expression:$e = \frac{1}{2} B \omega (l^2 + L^2)$

When a $J$-shaped conducting rod is rotating in its own plane with constant angular velocity $\omega$,about one of its ends $P$,in a uniform magnetic field $\vec B$ (directed normally into the plane of the paper),then the magnitude of the emf induced across it will be:

Similar Questions

If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$ and if $px^2+qx+r=0$ has roots $\frac{1-\alpha}{\alpha}$ and $\frac{1-\beta}{\beta}$,then $r$ is equal to

Which of the following is the most basic oxide?

Enthalpy of formation of $HF$ and $HCl$ are $-161 \ kJ$ and $-92 \ kJ$ respectively. Which of the following statements is incorrect?

$A$ coil of $n$ turns and resistance $R \ \Omega$ is connected in series with a resistance $R/2$. The combination is moved for time $t$ seconds through a magnetic flux change from $\phi_{1}$ to $\phi_{2}$. The induced current in the circuit is:

The full form of $NAD$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module