Q. No.A wooden stick of length is rotated about an end with constant angular velocity in a uniform magnetic field B perpendicular to the plane of motion. If the upper one third of its length is coated with copper, the potential difference across the whole length of the stick is –
1.
2.
3.
4.
An ideal inductor-resistor-battery circuit is switched on at \(t=0~\text{s}\). At time \(t\), the current is \(i=i_0\left(1-e^{\left(-\frac{t}{\tau}\right)}\right)\text{A}\), where \(i_0\) is the steady-state value. The time at which the current becomes \(0.5i_0\) is: [Given \(\text{ln}(2)= 0.693\)]
1. \(6.93 \times 10^3 ~\text{s}\)
2. \(6.93~\text{ms}\)
3. \(69.3~\text{s}\)
4. \(6.93~\text{s}\)
The resistance in the following circuit is increased at a particular instant. At this instant the value of resistance is \(10~\Omega.\) The current in the circuit will be:
| 1. | \(i = 0.5~\text{A}\) | 2. | \(i > 0.5~\text{A}\) |
| 3. | \(i < 0.5~\text{A}\) | 4. | \(i = 0\) |
| 1. | \(2~\text{A}\) | 2. | \(0.25~\text{A}\) |
| 3. | \(1.5~\text{A}\) | 4. | \(1~\text{A}\) |
A circular loop of radius R carrying current I lies in the x-y plane with its centre at the origin. The total magnetic flux through the x-y plane is
1. Directly proportional to I
2. Directly proportional to R
3. Directly proportional to R2
4. Zero
In which of the following devices, the eddy current effect is not used?
1. Electric heater
2. Induction furnace
3. Magnetic braking in train
4. Electromagnet
1. \(0.125 \pi~ \text{mV}\)
2. \(125 \pi ~\text{mV}\)
3. \(125 \pi~\text{V}\)
4. \(12.5 \pi~\text{mV}\)
1. \(1:2\)
2. \(2:1\)
3. \(8:1\)
4. \(1:8\)
1. \(2~\text{H}\)
2. \(4~\text{H}\)
3. \(8~\text{H}\)
4. \(12~\text{H}\)
A long solenoid of diameter \(0.1\) m has \(2 \times 10^4\) turns per meter. At the center of the solenoid, a coil of \(100\) turns and radius \(0.01\) m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to \(0\) A from \(4\) A in \(0.05\) s. If the resistance of the coil is \(10\pi^2~\Omega\), then the total charge flowing through the coil during this time is:
1. \(16~\mu \text{C}\)
2. \(32~\mu \text{C}\)
3. \(16\pi~\mu \text{C}\)
4. \(32\pi~\mu \text{C}\)
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