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.
Assertion (A): Inductance coil are made of copper.
Reason (R): Induced current is more in wire having less resistance.
Inductance coils are made of copper due to its low resistivity, minimizing energy loss. Low resistance allows more induced current for a given EMF (by \(I = V/R\)). Both Assertion (A) and Reason (R) are true, and R explains A.
Assertion (A): Change in magnetic flux w.r.t. time produces an induced emf.
Reason (R): Faraday established induced emf experimentally.
Assertion (A) is true based on Faraday's Law of electromagnetic induction, \( \epsilon = -\frac{d\Phi_B}{dt} \). Reason (R) is also true as Faraday's experiments confirmed this. (R) correctly explains (A).
Assertion (A): When a coil is rotated in a uniform magnetic field about an axis perpendicular to the field, emf is induced in it which is maximum for the orientation of coil in which magnetic flux through the coil is zero.
Reason (R): In an electric generator, electrical energy is generated by rotating a coil in a magnetic field.
Assertion (A) is true because \( \epsilon = BA\omega sin(\omega t) \), which is max when \( \Phi_B = BA cos(\omega t) = 0 \). Reason (R) is also true, describing generators. However, (R) is an application and doesn't explain the condition for maximum emf in (A).
Assertion (A): Only a change of magnetic flux with time, will maintain an induced current in the coil.
Reason (R): The presence of a large magnetic flux will maintain an induced current in the coil.
Assertion (A) is true based on Faraday's Law, which states that induced current is generated only by a change in magnetic flux. Reason (R) is false because a constant magnetic flux, regardless of its magnitude, does not induce a current.