1
JEE Main 2022 (Online) 27th July Evening Shift
Numerical
+4
-1

A conducting circular loop is placed in $$X-Y$$ plane in presence of magnetic field $$\overrightarrow{\mathrm{B}}=\left(3 \mathrm{t}^{3} \,\hat{j}+3 \mathrm{t}^{2}\, \hat{k}\right)$$ in SI unit. If the radius of the loop is $$1 \mathrm{~m}$$, the induced emf in the loop, at time, $$\mathrm{t}=2 \mathrm{~s}$$ is $$\mathrm{n} \pi \,\mathrm{V}$$. The value of $$\mathrm{n}$$ is ___________.

2
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1

In a coil of resistance $$8 \,\Omega$$, the magnetic flux due to an external magnetic field varies with time as $$\phi=\frac{2}{3}\left(9-t^{2}\right)$$. The value of total heat produced in the coil, till the flux becomes zero, will be _____________ $$J$$.

3
JEE Main 2022 (Online) 25th July Evening Shift
Numerical
+4
-1

Magnetic flux (in weber) in a closed circuit of resistance 20 $$\Omega$$ varies with time t(s) at $$\phi$$ = 8t2 $$-$$ 9t + 5. The magnitude of the induced current at t = 0.25 s will be ____________ mA.

4
JEE Main 2022 (Online) 27th June Evening Shift
Numerical
+4
-1

A metallic rod of length 20 cm is placed in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth's magnetic field at that place is 4 $$\times$$ 10$$-$$3 T and the angle of dip is 45$$^\circ$$. The emf induced in the rod is ___________ mV.