Looking for classes? Ksquare Career Institute, Bengaluru →
A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate $\frac{d\vec{B}}{dt}$. Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figure below. Then the e.m.f. generated is:
A
$-\frac{d\vec{B}}{dt}\pi R^2$ in loop 1 and zero in loop 2
B
$-\frac{d\vec{B}}{dt}\pi r^2$ in loop 1 and zero in loop 2
C
Zero in loop 1 and zero in loop 2
D
$-\frac{d\vec{B}}{dt}\pi r^2$ in loop 1 and $-\frac{d\vec{B}}{dt}\pi r^2$ in loop 2
Explanation
Only the flux actually enclosed changes.
Detailed Solution
For loop 1: $\varepsilon_{ind} = -A\left(\frac{dB}{dt}\right)\cos0^\circ = -\pi r^2\left(\frac{dB}{dt}\right)$ (only area $\pi r^2$ has field)
For loop 2: $\varepsilon_{ind} = 0$, as there is no flux linkage.
For loop 2: $\varepsilon_{ind} = 0$, as there is no flux linkage.