Q. No.A metallic ring connected to a rod oscillates freely like a pendulum. If now a magnetic field is applied in the horizontal direction so that the pendulum now swings through the field, the pendulum will
(1) Keep oscillating with the old-time period
(2) Keep oscillating with a smaller time period
(3) Keep oscillating with a larger time period
(4) Come to rest very soon
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A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A magnetic induction B constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere. The current induced in the loop is
(1) clockwise
(2) anticlockwise
(3) anticlockwise
(4) Zero
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A conducting square frame of side \(a\) and a long straight wire carrying current \(i\) are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity \(v\). The emf induced in the frame will be proportional to:
1. \(\frac{1}{x^2}\)
2. \(\frac{1}{(2x-a)^2}\)
3. \(\frac{1}{(2x+a)^2}\)
4. \(\frac{1}{(2x-a)\times (2x+a)}\)
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A metal rod moves at a constant velocity in a direction perpendicular to its length. A constant, uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement (s) from the following :
1. The entire rod is at the same electric potential
2. There is an electric field in the rod
3. The electric potential is highest at the center of the rod and decreases towards its ends
4. The electric potential is lowest at the center of the rod and increases towards its ends.
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A series combination of inductance (L) and resistance (R) is connected to a battery of emf E. The final value of current depends on –
1. L and R
2. E and R
3. E and L
4. E, L, and R
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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
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A conducting rod of length 2l is rotating with constant angular speed about its perpendicular bisector. A uniform magnetic field exists parallel to the axis of rotation. The e.m.f. induced between two ends of the rod is
(1) BΩl2
(2)
(3)
(4) Zero
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In the figure shown a square loop \(PQRS\) of side \(a\) and resistance \(r\) is placed near an infinitely long wire carrying a constant current \(I\). The sides \(PQ\) and \(RS\) are parallel to the wire. The wire and the loop are in the same plane. The loop is rotated by \(180^{\circ}\) about an axis parallel to the long wire and passing through the midpoints of the side \(QR\) and \(PS.\) The total amount of charge which passes through any point of the loop during rotation is:
| 1. | \(\frac{\mu _{0}Ia}{2\pi r}~\mathrm{ln}(2)\) |
| 2. | \(\frac{\mu _{0}Ia}{\pi r}~\mathrm{ln}(2) \) |
| 3. | \(\frac{\mu _{0}Ia^2}{2\pi r}\) |
| 4. | cannot be found because the time of rotation not given. |
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A long solenoid of diameter \(0.1\) m has \(2\times 10^{4}\) turns per meter. At the centre of the solenoid, a coil of \(100\) turns and a radius of \(0.01\) m is placed with its axis coinciding with the solenoid's axis. The current in the solenoid reduces at a constant rate from \(0\) A to \(4\) A in \(0.05\) s. If the resistance of the coil is \(10\pi^2~\Omega\), the total charge flowing through the coil during this time is:
| 1. | \(32\pi~\mu\text{C}\) | 2. | \(16~\mu\text{C}\) |
| 3. | \(32~\mu\text{C}\) | 4. | \(16\pi~\mu\text{C}\) |
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A small magnet is along the axis of a coil and its distance from the coil is 80 cm. In this position the flux linked with the coil are weber turns. If the coil is displaced 40 cm towards the magnet in 0.08 second, then the induced emf produced in the coil will be -
1. 0.5 mV
2. 1 mV
3. 7 mV
4. 3.5 mV
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