Q. No.The following figure shows two copper rods moving with the same velocity parallel to a long straight wire carrying current. If the induced emf in rod AB is \(\mathrm{E}\), the Induced emf in rod CD is:
1. \(\mathrm{E}\)
2. \(\mathrm{E}\cos \theta\)
3. \(\mathrm{E}\sin\theta\)
4. \(0\)
Subtopic: Â Motional emf |
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A triangular wire frame, in the form of an equilateral triangle \(PQR\) moves with a uniform velocity into a region where there is a uniform magnetic field \(B\). The edge \(PQ\) is parallel to the boundary of the region and the velocity \(v\) is perpendicular to it. The emf(\(E\)) induced within the frame is plotted as a function of time \(t,\) starting from when the frame enters the magnetic field. \(E\) is given by:
| 1. | \(Bv^2t\) | 2. | \(2Bv^2t\) |
| 3. | \(\dfrac{\sqrt3}{2}Bv^2t\) | 4. | \(\dfrac{2}{\sqrt3}Bv^2t\) |
Subtopic: Â Motional emf |
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A circular wire of radius \(R\) is placed in a uniform magnetic field \(B,\) which acts into the plane as shown. The wire is given a half-turn about a diameter. The resistance per unit length of the wire is \(\lambda.\) The total charge flowing through the wire is:
| 1. | \(\dfrac{2BR}{\lambda}\) | 2. | \(\dfrac{BR}{\lambda}\) |
| 3. | \(\dfrac{BR}{2\lambda}\) | 4. | zero |
Subtopic: Â Motional emf |
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Suppose a long rectangular loop of width \(w\) is moving along the \(x\)-direction with its left arm in a magnetic field perpendicular to the plane of the loop (see figure). The resistance of the loop is zero and it has an inductance \(L.\) At time, \(t= 0,\) its left arm passes the origin, \(O.\)
If for \(t\geq0,\) the current in the loop is \(I\) and the distance of its left arm from the origin is \(x,\) then \(I\) versus \(x\) graph would be:
If for \(t\geq0,\) the current in the loop is \(I\) and the distance of its left arm from the origin is \(x,\) then \(I\) versus \(x\) graph would be:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Â Motional emf |
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A conducting rod of mass \(m\) and length \(l\) is free to move without friction on two parallel long conducting rails, as shown below. There is a resistance \(R\) across the rails and in the entire space around there is a uniform magnetic field \(B\) normal to the plane of the rod and the rails. The rod is given an impulsive velocity \(v_0.\)
Finally, the initial energy \(\dfrac{1}{2}mv^2_0,\)
| 1. | will be converted fully into heat energy in the resistor. |
| 2. | will enable the rod to continue to move with velocity \(v_2\) since the rails are frictionless. |
| 3. | will be converted fully into magnetic energy due to induced current. |
| 4. | will be converted into the work done against the magnetic field. |
Subtopic: Â Motional emf |
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Rings are rotated and translated in a uniform magnetic field as shown in the figure. Arrange the magnitude of emf induced across \(AB\):
| 1. | \(\mathrm{emf_{a}<emf_{b}<emf_{c}}\) |
| 2. | \(\mathrm{emf_{a}=emf_{b}<emf_{c}}\) |
| 3. | \(\mathrm{emf_{a}={emf}_{c}<{emf}_{b}}\) |
| 4. | \(\mathrm{emf_{a}<emf_{b}={emf}_{c}}\) |
Subtopic: Â Motional emf |
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A wire, bent into the shape of a right angled triangle \(PQR,\) lies with its side \(PR\) parallel to a current carrying wire, and side \(QR\) perpendicular to it. The loop lies in the plane of the wire. EMF induced in the loop when it is moved with constant speed along \(PR\) is \(\varepsilon_1\) and it is \(\varepsilon_2\) when moved along \(QR\) with the same constant speed. Then,
1. \(\varepsilon_1=0,\varepsilon_2\neq0\)
2. \(\varepsilon_1\neq0,\varepsilon_2=0\)
3. \(\varepsilon_1=0,\varepsilon_2=0\)
4. \(\varepsilon_1\neq0,\varepsilon_2\neq0\)
1. \(\varepsilon_1=0,\varepsilon_2\neq0\)
2. \(\varepsilon_1\neq0,\varepsilon_2=0\)
3. \(\varepsilon_1=0,\varepsilon_2=0\)
4. \(\varepsilon_1\neq0,\varepsilon_2\neq0\)
Subtopic: Â Motional emf |
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A conducting circular loop is moving in a region of uniform and constant magnetic field as shown in the figure. The potential difference between points \(P\) and \(Q\) is:
1. zero
2. \(2B_0Rv\)
3. \(B_0Rv\)
4. \(\dfrac{B_0Rv}{2}\)
1. zero
2. \(2B_0Rv\)
3. \(B_0Rv\)
4. \(\dfrac{B_0Rv}{2}\)
Subtopic: Â Motional emf |
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A metallic rod of length \(3~\text{m}\) rotates with an angular speed of \(4~\text{rad/s}\) in a uniform magnetic field. The field makes an angle of \(30^{\circ}\) with the plane of rotation. The emf induced across the rod is \(72~\text{mV}\). The magnitude of the field is:
1. \(4 \times 10^{-3}~\text{T}\)
2. \(8 \times 10^{-3}~\text{T}\)
3. \(16 \times 10^{-3}~\text{T}\)
4. \(48 \times 10^{-3}~\text{T}\)
1. \(4 \times 10^{-3}~\text{T}\)
2. \(8 \times 10^{-3}~\text{T}\)
3. \(16 \times 10^{-3}~\text{T}\)
4. \(48 \times 10^{-3}~\text{T}\)
Subtopic: Â Motional emf |
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An \(L\)-shaped rod \((ABC;AB=BC=a)\) moves in its own plane with a velocity \(v\) parallel to \(AB.\) There is a uniform magnetic field \(B\) acting into the plane as shown. The emf developed between \(A,C\) is:
1. \(Bav\)
2. \(\sqrt2Bav\)
3. \(\dfrac{Bav}{2}\)
4. zero
1. \(Bav\)
2. \(\sqrt2Bav\)
3. \(\dfrac{Bav}{2}\)
4. zero
Subtopic: Â Motional emf |
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