A wire loop enclosing a semi-circle of radius | vedclass

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

Question

(A) The magnetic flux $\phi_B$ through the part of the loop inside the magnetic field is given by the area of the sector of the circle within the fiel

Vedclass · Accepted Answer

$\frac{B R^2}{2} \omega$

Vedclass · Answer

(A) The magnetic flux $\phi_B$ through the part of the loop inside the magnetic field is given by the area of the sector of the circle within the field multiplied by the magnetic field strength $B$.Let $	heta$ be the angle of the sector inside the magnetic field at any time $t$. The area of this sector is $A = \frac{1}{2} R^2 	heta$.The magnetic flux is $\phi_B = B A = B \left( \frac{1}{2} R^2 	heta ight)$.According to Faraday's law of induction,the magnitude of the induced emf $\varepsilon$ is given by $\varepsilon = \left| \frac{d \phi_B}{dt} ight|$.Since the loop rotates with angular velocity $\omega$,we have $\frac{d 	heta}{dt} = \omega$.Therefore,$\varepsilon = \left| \frac{d}{dt} \left( \frac{1}{2} B R^2 	heta ight) ight| = \frac{1}{2} B R^2 \left| \frac{d 	heta}{dt} ight| = \frac{B R^2 \omega}{2}$.

Similar Questions

$A$ coil has $1000$ turns and $500 \text{ cm}^2$ as its area. The plane of the coil is placed at right angles to a magnetic induction field of $2 \times 10^{-5} \text{ Wb/m}^2$. The coil is rotated through $180^{\circ}$ in $0.2 \text{ s}$. The average emf induced in the coil,in $\text{mV}$,is

An $emf$ of $0.08\,V$ is induced in a metal rod of length $10\,cm$ held normal to a uniform magnetic field of $0.4\,T$,when it moves with a velocity of .......... $m/s$.

$A$ copper rod $AB$ of length $L$,pivoted at one end $A$,rotates at a constant angular velocity $\omega$,at right angles to a uniform magnetic field of induction $B$. The e.m.f. developed between the midpoint $C$ of the rod and end $B$ is

When a wire loop is rotated in a magnetic field,the direction of induced $e.m.f.$ changes once in each........$revolution$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module