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Q. No.A square wire loop of resistance \(0.5\) \(\Omega\)/m, having a side \(10\) cm and made of \(100\) turns is suddenly flipped in a magnetic field \(B,\) which is perpendicular to the plane of the loop. A charge of \(2\times10^{-4}
\) C passes through the loop. The magnetic field \(B\) has the magnitude of:
1. \(2\times10^{-6}
\) T
2. \(4\times10^{-6}
\) T
3. \(2\times10^{-3}
\) T
4. \(4\times10^{-3}
\) T
Subtopic: Magnetic Flux |
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A rectangular loop of conducting wire is bent symmetrically so that its two plane halves are inclined at right angles with respect to each other (i.e. \(\angle \text { PQR }=\angle S T U=90^{\circ}\)). Every segment has a length 'a' (PQ = QR = RS = ... = UP = a). A uniform time-dependent magnetic field B(t) acts on the loop, making an angle '\(\alpha\)' with the lower half of the loop and '\(90^o - \alpha \)' with the upper half. The EMF induced in the loop is proportional to:
\(1.~ (\cos \alpha+\sin \alpha) \frac{d B}{d t}\\ 2.~ (\cos \alpha-\sin \alpha) \frac{d B}{d t}\\ 3.~ (\tan \alpha+\cot \alpha) \frac{d B}{d t}\\ 4.~ (\tan \alpha-\cot \alpha) \frac{dB}{d t}\)
\(1.~ (\cos \alpha+\sin \alpha) \frac{d B}{d t}\\ 2.~ (\cos \alpha-\sin \alpha) \frac{d B}{d t}\\ 3.~ (\tan \alpha+\cot \alpha) \frac{d B}{d t}\\ 4.~ (\tan \alpha-\cot \alpha) \frac{dB}{d t}\)
Subtopic: Faraday's Law & Lenz Law |
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A circular loop of radius \(\mathrm{R}\), enters a region of uniform magnetic field \(\mathrm{B}\) as shown in the diagram. The field \((\mathrm{B})\) is perpendicular to the plane of the loop while the velocity of the loop,\(\mathrm{v}\), is along its plane. The induced EMF:
| 1. | increases continuously. |
| 2. | decreases continuously. |
| 3. | first increases and then decreases. |
| 4. | remains constant throughout. |
Subtopic: Faraday's Law & Lenz Law |
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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. \(\frac{\sqrt3}{2}Bv^2t\)
4. \(\frac{2}{\sqrt3}Bv^2t\)
1. \(Bv^2t\)
2. \(2Bv^2t\)
3. \(\frac{\sqrt3}{2}Bv^2t\)
4. \(\frac{2}{\sqrt3}Bv^2t\)
Subtopic: Motional emf |
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A small solenoid is kept inside a much larger solenoid, with their axes parallel to each other. The small solenoid has a cross-sectional radius \(r_1,\) length \(l_1\) and the total number of turns \(N_1.\) The corresponding quantities for the larger solenoid are: \(r_2,~ l_2,~ N_2\) respectively.
Their mutual inductance is (nearly) given by:
1. \(\frac{\mu_0\pi r^2_1N_1N_2}{l_2}\)
2. \(\frac{\mu_0\pi r^2_1N_1N_2}{\sqrt{l_1l_2}}\)
3. \(\frac{\mu_0\pi r^2_1N_1N_2}{l_1}\)
4. \(\frac{\mu_0~\pi r_1r_2N_1N_2}{\sqrt{l_1}}\)
Their mutual inductance is (nearly) given by:
1. \(\frac{\mu_0\pi r^2_1N_1N_2}{l_2}\)
2. \(\frac{\mu_0\pi r^2_1N_1N_2}{\sqrt{l_1l_2}}\)
3. \(\frac{\mu_0\pi r^2_1N_1N_2}{l_1}\)
4. \(\frac{\mu_0~\pi r_1r_2N_1N_2}{\sqrt{l_1}}\)
Subtopic: Mutual Inductance |
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A rod \(\mathrm{XY}\) of length \(l\) is placed in a uniform magnetic field \(B\), as shown in the diagram. The rod moves with a velocity \(v\), making an angle of \(60^\circ\) with its length. The emf induced in the rod is:
| 1. | \(vBl\) | 2. | \(vBl \over 2\) |
| 3. | \({\sqrt 3 \over 2}vBl\) | 4. | \({1 \over \sqrt 3}vBl\) |
Subtopic: Motional emf |
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A straight horizontal wire of mass \(m\) and length \(l,\) and having a negligible resistance can slide freely on a pair of conducting parallel rails, placed vertically. The rails are connected at the top by a capacitor \(C.\) A uniform magnetic field \(B\) exists in the region, perpendicular to the plane of the rails. The wire:
| 1. | falls with uniform velocity. |
| 2. | accelerates down with acceleration less than \(g\). |
| 3. | accelerates down with acceleration equal to \(g\). |
| 4. | moves down and eventually comes to rest. |
Subtopic: Motional emf |
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The self-inductance of a long solenoid of cross-section \(A,\) total length \(L\) and total number of turns \(N,\) is (approximately):
1. \(\frac{\mu_0A}{L}\cdot N\)
2. \(\frac{\mu_0A}{L}\cdot N^2\)
3. \(\frac{\mu_0L^3}{A}\cdot N\)
4. \(\frac{\mu_0L^3}{A}\cdot N^2\)
1. \(\frac{\mu_0A}{L}\cdot N\)
2. \(\frac{\mu_0A}{L}\cdot N^2\)
3. \(\frac{\mu_0L^3}{A}\cdot N\)
4. \(\frac{\mu_0L^3}{A}\cdot N^2\)
Subtopic: Self - Inductance |
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A conducting circular wire of radius \(r\) is moving with constant velocity \(v\) towards the right in a uniform magnetic field \(B.\) We consider two points \(X,Y\) such that chord \(XY\) is perpendicular to the velocity \(v\) and is at a distance \(x\) from the centre \((O)\) of the circle. The EMF induced between \(X,Y\) is \(\varepsilon.\) Then, \(\varepsilon\) is proportional to:
1. \(x\)
2. \(\sqrt{r^2-x^2}\)
3. \(r\)
4. \(x\sqrt{r^2-x^2}\)
1. \(x\)
2. \(\sqrt{r^2-x^2}\)
3. \(r\)
4. \(x\sqrt{r^2-x^2}\)
Subtopic: 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. \(\frac{Bav}{2}\)
4. zero
1. \(Bav\)
2. \(\sqrt2Bav\)
3. \(\frac{Bav}{2}\)
4. zero
Subtopic: Motional emf |
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