A conducting wire bent in the shape of a semi | vedclass

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

Question

(D) The induced emf in a moving conductor is given by $e = B l_{eff} v \sin(	heta)$,where $l_{eff}$ is the displacement vector between the two ends o

Vedclass · Accepted Answer

$\frac{\sqrt{2}}{\pi}$

Vedclass · Answer

(D) The induced emf in a moving conductor is given by $e = B l_{eff} v \sin(	heta)$,where $l_{eff}$ is the displacement vector between the two ends of the conductor.For a semicircular wire of length $L$,the radius $r$ is given by $L = \pi r$,so $r = \frac{L}{\pi}$.The effective length $l_{eff}$ (the straight-line distance between the two ends) is the diameter of the semicircle,$l_{eff} = 2r = \frac{2L}{\pi}$.The velocity $v$ makes an angle of $45^{\circ}$ with the diameter (the effective length vector).Substituting these values into the emf formula:$e = B 	imes (\frac{2L}{\pi}) 	imes v 	imes \sin(45^{\circ})$$e = B 	imes \frac{2L}{\pi} 	imes v 	imes \frac{1}{\sqrt{2}}$$e = \frac{\sqrt{2}}{\pi} B v L$Comparing this with the given expression $\Phi = \alpha(B v L)$,we find $\alpha = \frac{\sqrt{2}}{\pi}$.

Similar Questions

Two metallic rings of radius $R$ are rolling on a metallic rod. $A$ magnetic field of magnitude $B$ is applied in the region. The magnitude of the potential difference between point $A$ and point $C$ on the two rings (as shown) will be:

$A$ conducting rod $PQ$ of length $L = 1.0 \, m$ is moving with a uniform speed $v = 2 \, m/s$ in a uniform magnetic field $B = 4.0 \, T$ directed into the paper. $A$ capacitor of capacity $C = 10 \, \mu F$ is connected as shown in the figure. Then:

$A$ conducting rod $AC$ of length $4l$ is rotated about a point $O$ in a uniform magnetic field $\vec B$ directed into the paper. $AO = l$ and $OC = 3l$. Then:

$A$ $800$ turn coil of effective area $0.05\; m^{2}$ is kept perpendicular to a magnetic field $5 \times 10^{-5}\; T$. When the plane of the coil is rotated by $90^{\circ}$ around any of its coplanar axes in $0.1\; s$,the $emf$ induced in the coil will be.....$V$

Vedclass Test Series

Exam Paper Generator

Online Exam Module