A rod having length \(l\) and resistance \(R_0\) is moving with speed \(v\) as shown in the figure. The current through the rod is:
1. \(\frac{B l v}{\frac{R_{1} R_{2}}{R_{1} + R_{2}} + R_{0}}\)
2. \(\frac{Blv}{\left(\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{o}}\right)^{2}}\)
3. \(\frac{B l v}{R_{1} + R_{2} + R_{0}}\)
4. \(\frac{B l v}{\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{0}}}\)
A solenoid of inductance L and resistance R is connected to a battery of e.m.f. E. Maximum value of magnetic energy stored in the inductor is:
The coefficient of mutual inductance between two coils depends upon:
1. | medium between coils |
2. | separation between coils |
3. | orientation of coils |
4. | All of these |
A small square loop of wire of side 'l' is placed inside a large square loop of side 'L' (Ll). If the loops are coplanar and their centres coincide, the mutual inductance of the system is directly proportional to:
1. L/l
2. l/L
3. L2/l
4. l2/L
Two coils have a mutual inductance of 5 mH. The current changes in the first coil according to the equation \(I=I_{0}cos\omega t,\) where \(I_{0}=10~A\) and = 100 rad/s. The maximum value of e.m.f. induced in the second coil is:
1. 5 Volt
2. 2 Volt
3. 4 Volt
4. Volt
Eddy currents are used in:
1. Induction furnace
2. Electromagnetic brakes
3. Speedometers
4. All of these
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. \(t=5~\text{s}\)
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. \(\frac{\mu_{0} l}{2} \frac{R^{2}}{l}\)
2. \(\frac{\mu_{0} I l^{2}}{2 R}\)
3. \(\frac{\mu_{0} l \pi R^{2}}{2 l}\)
4. \(\frac{\mu_{0} \pi R^{2} I}{l}\)
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. | \(5 \pi \times 10^{-4}~\text{Wb}\) |
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. |