The magnetic flux linked with a coil, in webers, is given by the equations Φ = 3t² + 4t + 9. Then
the magnitude of induced e.m.f. at t = 2 second will be
The flux linked with a coil at any instant ‘t’ is given by Φ = 10t² – 50t + 250. The induced emf at t = 3 s is :
A coil having 500 square loops each of side 10 cm is placed normal to a magnetic flux which increases at the rate of 1.0 Tesla/second. The induced e.m.f. in volts is :
A coil has 200 turns and area of \(70\text{ cm}^2\). The magnetic field perpendicular to the plane of the coil is \(0.3\text{ Wb m}^{-2}\) and takes \(0.1\text{ s}\) to rotate through \(180^\circ\). The value of the induced E.M.F. will be:
Change in flux \(\Delta \Phi = 2NBA = 2 \times 200 \times 0.3 \times (70 \times 10^{-4}) = 0.84\text{ Wb}\). Induced EMF is \(e = \frac{\Delta \Phi}{\Delta t} = \frac{0.84}{0.1} = 8.4\text{ V}\).
If a current is passed through a spring then the spring will:
Current flows in the same direction in adjacent turns of the spring. Since parallel currents in the same direction attract each other, the turns of the spring are pulled closer, causing the spring to compress.
Assertion (A): The electric field created by time-varying magnetic field is non-conservative.
Reason (R): The line integral of induced electric field in a closed loop is always equal to zero.
Electric field created by time-varying magnetic field is non-conservative, which means its line integral around a closed loop is non-zero (\(\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt}\)). Hence, Assertion is true but Reason is false.
Two coils have mutual inductance \(0.005\text{ H}\). The current changes in the first coil according to equation \(I = I_0 \sin \omega t\), where \(I_0 = 10\text{ A}\) and \(\omega = 100\pi\text{ rad/s}\). The maximum value of EMF in the second coil is:
Induced EMF is \(e = M \frac{dI}{dt} = M I_0 \omega \cos \omega t\). Maximum EMF \(e_{max} = M I_0 \omega = 0.005 \times 10 \times 100\pi = 5\pi\text{ V}\).
If the flux associated with a coil varies at the rate of \(2\text{ Wb/min}\), then the induced emf in the coil is
From Faraday's law, the induced electromotive force is \(e = \frac{dPhi}{dt}\). Converting minutes to seconds: \(e = \frac{2\text{ Wb}}{60\text{ s}} = \frac{1}{30}\text{ V}\).
A coil has a self-inductance of 0.02 H. The current through it, is allowed to change at the rate of 4 A in \(2 \times 10^{-2}\text{ s}\). The e.m.f induced in the coil will be
Formula: \(e = L \frac{dI}{dt}\). Substituting \(L = 0.02\text{ H}\), \(dI = 4\text{ A}\) and \(dt = 2 \times 10^{-2}\text{ s}\), we get \(e = 0.02 \times 200 = 4\text{ V}\).
Assertion (A): At the instant when magnetic flux is zero, emf induced in the coil is maximum when it is rotating in uniform magnetic field w.r.t. axis in the plane of coil.
Reason (R): emf induced in the coil is equal to rate of change of magnetic flux.
Induced emf is \(E = -d\phi/dt = BA\omega sin(\omega t)\). Magnetic flux is \(\phi = BA cos(\omega t)\). When \(\phi = 0\), \(cos(\omega t) = 0\), which implies \(sin(\omega t) = 1\). Thus, \(E\) is maximum. Both A and R are true, and R correctly explains A.