The magnetic flux linked with a coil varies with time as \(\phi = 2t^2-6t+5,\) where \(\phi \) is in Weber and \(t\) is in seconds. The induced current is zero at:

A coil having number of turns \(N\) and cross-sectional area \(A\) is rotated in a uniform magnetic field \(B\) with an angular velocity \(\omega\). The maximum value of the emf induced in it is:
1. \(\frac{NBA}{\omega}\)
2. \(NBAω\)
3. \(\frac{NBA}{\omega^{2}}\)
4. \(NBAω^{2}\)

The current in a coil varies with time \(t\) as \(I= 3 t^{2} +2t\). If the inductance of coil be \(10\) mH, the value of induced emf at \(t=2~\text{s}\) will be:
1. \(0.14~\text{V}\)
2. \(0.12~\text{V}\)
3. \(0.11~\text{V}\)
4. \(0.13~\text{V}\)

In a circuit with a coil of resistance \(2~\Omega\), the magnetic flux changes from \(2.0\) Wb to \(10.0\) Wb in \(0.2~\text{s}\). The charge that flows in the coil during this time is:
1. \(5.0~\text{C}\)
2. \(4.0~\text{C}\)
3. \(1.0~\text{C}\)
4. \(0.8~\text{C}\)

A bar magnet is released along the vertical axis of the conducting coil. The acceleration of the bar magnet is:

A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is:

An aluminium ring \(B\) faces an electromagnet \(A\). If the current \(I\) through \(A\) can be altered, then:

A conducting circular loop is placed in a uniform magnetic field of \(0.04\) T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a rate of \(2\) mm/s. The induced emf in the loop when the radius is \(2\) cm is:
1. \(3.2\pi ~\mu \text{V}\)

2. \(4.8\pi ~\mu\text{V}\)

3. \(0.8\pi ~\mu \text{V}\)

4. \(1.6\pi ~\mu \text{V}\)

A magnet is brought towards a coil first (i) speedily (ii) slowly. It can be concluded that the induced e.m.f. and the induced charge in the two cases, will be respectively: