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. \(\frac{B l v}{\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{0}}}\)
\(1 .\) \(\frac{E^{2}}{2 R}\)
\(2 .\) \(\frac{E^{2} L}{2 R^{2}}\)
\(3 .\) \(\frac{E^{2} L}{R}\) \(\)
\(4 .\) \(\frac{E^{2} L}{2 R}\)
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 |
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 \(I_{0}=10~\text{A}\)and\(\omega = 100\pi ~\text{rad/s}\). The maximum value of emf induced in the second coil is:
1. \(5\pi\) Volt
2. \(2\pi\) Volt
3. \(4\pi\) Volt
4. \(\pi\) 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. |