Q. No.A circular disc of the radius \(0.2~\text m\) is placed in a uniform magnetic field of induction \(\dfrac{1}{\pi} \left(\dfrac{\text{Wb}}{\text{m}^{2}}\right)\) in such a way that its axis makes an angle of \(60^{\circ}\) with \(\vec {B}.\) The magnetic flux linked to the disc will be:
1. \(0.02~\text{Wb}\)
2. \(0.06~\text{Wb}\)
3. \(0.08~\text{Wb}\)
4. \(0.01~\text{Wb}\)
If a current is passed through a circular loop of radius \(R\) then magnetic flux through a coplanar square loop of side \(l\) as shown in the figure \((l<<R)\) is:
1. \(\dfrac{\mu_{0} I}{2} \dfrac{R^{2}}{l}\)
2. \(\dfrac{\mu_{0} I l^{2}}{2 R}\)
3. \(\dfrac{\mu_{0}I \pi R^{2}}{2 l}\)
4. \(\dfrac{\mu_{0} \pi R^{2} I}{l}\)
The radius of a loop as shown in the figure is \(10~\text{cm}.\) If the magnetic field is uniform and has a value \(10^{-2}~ \text{T},\) then the flux through the loop will be:
1. \(2 \pi \times 10^{-2}~\text{Wb}\)
2. \(3 \pi \times 10^{-4}~\text{Wb}\)
3. \(5 \pi \times 10^{-5}~\text{Wb}\)
4. \(5 \pi \times 10^{-4}~\text{Wb}\)
1. \(\left[ M L^2 T^{-2}A^{-1}\right]\)
2. \(\left[ M L^1 T^{-1}A^{-2}\right]\)
3. \(\left[ M L^2 T^{-3}A^{-1}\right]\)
4. \(\left[ M L^{-2} T^{-2}A^{-2}\right]\)
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:
| 1. | \(t=0\) | 2. | \(t= 1.5~\text{s}\) |
| 3. | \(t=3~\text{s}\) | 4. | \(t=5~\text{s}\) |
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. \(0.13~\text{V}\)
A bar magnet is released along the vertical axis of the conducting coil. The acceleration of the bar magnet is:
| 1. | greater than \(g\). | 2. | less than \(g\). |
| 3. | equal to \(g\). | 4. | zero. |
1. \(\frac{3 A_{0} B_{0}}{t}\)
2. \(\frac{4 A_{0} B_{0}}{t}\)
3. \(\frac{3 B_{0}}{A_{0} t}\)
4. \(\frac{4 B_{0}}{A_{0} t}\)
A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is:
| 1. | Twice per revolution | 2. | Four times per revolution |
| 3. | Six times per revolution | 4. | Once per revolution |
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