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Q. No.A metal “Slinky” can be used as a solenoid. The “Slinky” is stretched slightly, and a current is passed through it. Will the resulting magnetic field cause the “Slinky” to collapse or to stretch out further?
| 1. | collapse |
| 2. | stretch out further |
| 3. | neither, the magnetic field is zero outside a solenoid |
| 4. | the answer depends on the direction of the current |
Subtopic: Force between Current Carrying Wires |
Level 3: 35%-60%
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A conducting wire is bent into the form of a square \(ABCD,\) and electrical connections are established in two different ways:
The same potential difference is established between the two connected ends. Current is, however, allowed to take only a single path from the positive to the negative terminal by disconnecting the other path. Let the magnetic field at the centre in these cases be \(B_\text I,B_\text{II}.\) Then, \(\frac{B_\text I}{B_\text{II}}=\)
| (I) | at two adjacent vertices \(A,B\) |
| (II) | at two points \(A,C\) at the ends of a diagonal. |
| 1. | \(2\) | 2. | \(\dfrac12\) |
| 3. | \(\dfrac{1}{\sqrt2}\) | 4. | \(1\) |
Subtopic: Magnetic Field due to various cases |
Level 3: 35%-60%
Hints
A wire carrying a current \(I_0\) oriented along the vector \(\big(3\hat{i}+4\hat{j}\big)\) experiences a force per unit length of \(\big(4F\hat{i}-3F\hat{j}-F\hat{k}\big).\) The magnetic field \(\vec{ B}\) equals:
1. \(\dfrac{F}{I_0}\left(\hat{i}+\hat{j}\right)\)
2. \(\dfrac{5F}{I_0}\left(\hat{i}+\hat{j}+\hat{k}\right)\)
3. \(\dfrac{F}{I_0}\left(\hat{i}+\hat{j}+\hat{k}\right)\)
4. \(\dfrac{5F}{I_0}\hat{k}\)
Subtopic: Lorentz Force |
Level 3: 35%-60%
Hints
To ensure that the magnetic field is radial in a moving coil galvanometer:
| 1. | The number of turns in the coil is increased. |
| 2. | The magnet is taken in the form of a horse-shoe. |
| 3. | The poles are cut cylindrically. |
| 4. | The coil is wound on an aluminum frame. |
Subtopic: Moving Coil Galvanometer |
Level 3: 35%-60%
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A charged particle (charge: \(q\)) moves in a circular orbit in a uniform magnetic field, its orbit enclosing a magnetic flux \(\Phi.\) The angular momentum of the particle is:
| 1. | \(q\Phi\) | 2. | \(\dfrac{q\Phi}{2\pi}\) |
| 3. | \(\pi q\Phi\) | 4. | \(\dfrac{q\Phi}{\pi}\) |
Subtopic: Lorentz Force |
Level 3: 35%-60%
Hints
Given below are two statements:
| Statement I: | The magnetic field due to a segment \({d\vec l}\) of a current-carrying wire carrying a current, \(I\) is given by: \({d\vec B}=\dfrac{\mu_0}{4\pi}~I\left({d\vec l}\times\dfrac{\vec r}{r^3}\right ),\) where \(\vec{r}\) is the position vector of the field point with respect to the wire segment. |
| Statement II: | The magnetic field of a current-carrying wire is never parallel to the wire. |
| 1. | Statement I and Statement II are True and Statement I is the correct explanation of Statement II. |
| 2. | Statement I and Statement II are True and Statement I is not the correct explanation of Statement II. |
| 3. | Statement I is True, and Statement II is False. |
| 4. | Statement I is False, and Statement II is True. |
Subtopic: Biot-Savart Law |
Level 3: 35%-60%
Hints
Two small current-carrying loops carrying currents in the clockwise direction are placed in the same plane, separated by a distance \(d\) (which is much larger than the size of the loops). The two loops:
| 1. | attract each other. |
| 2. | repel each other. |
| 3. | exert no force on each other, but exert a torque. |
| 4. | neither exert any force nor any torque on each other. |
Subtopic: Current Carrying Loop: Force & Torque |
Level 3: 35%-60%
Hints
Two long straight wires carrying currents \(i_1, i_2\) are placed as shown in the figure, just avoiding contact. The separation between the wires is negligible, and the wires are aligned along \(x\) & \(y\) axes respectively.
The wire along the \(x\text-\)axis experiences:
The wire along the \(x\text-\)axis experiences:
| 1. | a force along \(+y\) axis only. |
| 2. | a force along \(-y\) axis. |
| 3. | zero force, but a torque. |
| 4. | no force and no torque. |
Subtopic: Force between Current Carrying Wires |
Level 3: 35%-60%
Hints
A metal rod \(PQ\) (carrying current from \(P\) to \(Q\)) is placed perpendicular to an infinitely long wire carrying a current \(i_0.\) If this arrangement lies in a horizontal plane, in which direction will the rod \(PQ\) rotate?
1. clockwise
2. anticlockwise
3. along the axis of \(PQ\)
4. it will not rotate
Subtopic: Force between Current Carrying Wires |
Level 3: 35%-60%
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A circular coil of radius \(r\) carries a current \(i\) and is placed in a uniform magnetic field \(B,\) with its plane parallel to the field. The magnitude of the torque acting on the coil is:
| 1. | zero | 2. | \(2\pi r i B\) |
| 3. | \(\pi r^2i B\) | 4. | \(2\pi r^2i B\) |
Subtopic: Current Carrying Loop: Force & Torque |
Level 3: 35%-60%
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