A metal rod of length 0.5 m moves with its length perpendicular to a uniform magnetic field of 0.2 T with a velocity of 3 ms-1. The induced emf in the rod is
0.3 V
Motional emf for a rod moving perpendicular to the field: \(\varepsilon = Blv\)
\(\varepsilon = 0.2 \times 0.5 \times 3\)
\(\varepsilon = 0.3\text{ V}\)
Hence, 0.3 V.
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Important Questions from Electricity and Magnetism
- A short bar magnet placed with its axis at $30^\circ$ with an external field of 800 Gauss, experiences a torque of 0.016 N.m. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} \text{ J}$. The value of $\alpha$ is ______.
- An electromagnetic wave of frequency $100\text{ MHz}$ propagates through a medium of conductivity, $\sigma = 10\text{ mho/m}$. The ratio of maximum conduction current density to maximum displacement current density is __________.
$\left[ \text{Take } \frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\text{ Nm}^2\text{/C}^2 \right]$ - An inductor stores $16\text{ J}$ of magnetic field energy and dissipates $32\text{ W}$ of thermal energy due to its resistance when an a.c. current of $2\text{ A}$ (rms) and frequency $50\text{ Hz}$ flows through it. The ratio of inductive reactance to its resistance is _________. ($\pi = 3.14$)
- A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of $60^\circ$ with vertical, then maximum induced EMF between the point of suspension and point of oscillation is ___________ mV. (Take $g = 10\text{ m/s}^2$)
Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for $V = 5\sin(100t)$ The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ___________ $\mu\text{F}$.
