Q. No.An insulated wire is wound so that it forms a flat coil with \(N=200\) turns. The radius of the innermost turns is \(r_1=3~\text{cm}\), and of the outermost turn \(r_2=6~\text{cm}\). If \(20~\text{mA}\) current flows in it then the magnetic moment will be \(\alpha\times10^{-2}~\text{Am}^2\). The value of \(\alpha\) is:
1. \(4.4\)
2. \(2.64\)
3. \(3.25\)
4. \(1.2\)
1. \(4.4\)
2. \(2.64\)
3. \(3.25\)
4. \(1.2\)
Subtopic: Ā Magnetic Moment |
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Match List-I with List-II.
Choose the correct answer from the options given below:
1. (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
2. (A)-(I), (B)-(IV), (C)-(II), (D)-(III)
3. (A)-(II), (B)-(I), (C)-(III), (D)-(IV)
4. (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
| List - I | List - II | ||
| (A) | Permeability of free space | (I) | \([ML^2T^{-2}]\) |
| (B) | Magnetic field | (II) | \([MT^{-2}A^{-1}]\) |
| (C) | Magnetic moment | (III) | \([MLT^{-2}A^{-2}]\) |
| (D) | Torsional constant | (IV) | \([L^2A]\) |
1. (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
2. (A)-(I), (B)-(IV), (C)-(II), (D)-(III)
3. (A)-(II), (B)-(I), (C)-(III), (D)-(IV)
4. (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
Subtopic: Ā Magnetic Moment |
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A coil having \(100\) turns, area of \(5 \times 10^{-3}~ \text m^2, \) carrying current of \(1 ~\text{mA}\) is placed in uniform magnetic field of \(0.20 ~\text{T}\) such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through \(90^\circ\) is \(x~\text{Ī¼J}\). Find the value of \(x\):
1. \(1\)
2. \(10\)
3. \(100\)
4. \(1000\)
1. \(1\)
2. \(10\)
3. \(100\)
4. \(1000\)
Subtopic: Ā Magnetic Moment |
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A circular coil having \(200\) turns, \(2.5 \times 10^{-4} \mathrm{~m}^2\) area and carrying \(100 ~\mu A\) current is placed in a uniform magnetic field of \(1\) \(T\). Initially the magnetic dipole moment \((\vec{M})\)was directed along \(\vec{B}\). Amount of work, required to rotate the coil through \(90^{\circ}\) from its initial orientation such that \((\vec{M})\) becomes perpendicular to \(\vec{B}\), is ______________________ \(\mu \mathrm{J} \).
1. \(0\)
2. \(5\)
3. \(10\)
4. \(50\)
1. \(0\)
2. \(5\)
3. \(10\)
4. \(50\)
Subtopic: Ā Magnetic Moment |
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The characteristics of two coils are given below:
If the magnetic moments of both Coil-\(A\) and Coil-\(B\) are equal, choose the correct relation:
1. \(2N_AI_A = N_BI_B\)
2. \(N_AI_A = N_BI_B\)
3. \(N_AI_A = 4N_BI_B\)
4. \(N_AI_A = 2N_BI_B\)
| Coil-\(A\) | Coil-\(B\) | |
| Radius | \(r_A = 10~ \text{cm}\) | \(r_A = 20~ \text{cm}\) |
| Number of turns | \(N_A\) | \(N_B\) |
| Current | \(I_A~\text{ampere}\) | \(I_B~\text{ampere}\) |
1. \(2N_AI_A = N_BI_B\)
2. \(N_AI_A = N_BI_B\)
3. \(N_AI_A = 4N_BI_B\)
4. \(N_AI_A = 2N_BI_B\)
Subtopic: Ā Magnetic Moment |
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Coil \(\mathrm{A}\) of radius \(10\) cm has \(N_A\) number of turns and \(I_A\) current is flowing through it. Coil \(\mathrm{B}\) of radius \(20\) cm has \(N_B\) number of turns and \(I_B\) current is flowing through it. If the magnetic dipole moment of both the coils is the same then:
1. \( I_A N_A=4 I_B N_B \)
2. \( 4 I_A N_A= I_B N_B\)
3. \( I_A N_A=2 I_B N_B \)
4. \( 2 I_A N_A= I_B N_B \)
1. \( I_A N_A=4 I_B N_B \)
2. \( 4 I_A N_A= I_B N_B\)
3. \( I_A N_A=2 I_B N_B \)
4. \( 2 I_A N_A= I_B N_B \)
Subtopic: Ā Magnetic Moment |
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Two concentric circular loops of radii \(r_1=30\) cm and \(r_2=50\) cm are placed in \(X\text-Y\) plane as shown in the figure. A current \(I=7\) A is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately:
1. \(\frac{7}{2} \hat k~\text{Am}^2\)
2. \(-\frac{7}{2} \hat k~\text{Am}^2\)
3. \( 7~ \hat k~\text{Am}^2\)
4. \( -7~ \hat k~\text{Am}^2\)
1. \(\frac{7}{2} \hat k~\text{Am}^2\)
2. \(-\frac{7}{2} \hat k~\text{Am}^2\)
3. \( 7~ \hat k~\text{Am}^2\)
4. \( -7~ \hat k~\text{Am}^2\)
Subtopic: Ā Magnetic Moment |
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Two short magnetic dipoles \(M_1\) and \(M_2\) each having a magnetic moment of \(1~ \text{Am}^2\) are placed at point \(O\) and \(P\) respectively. The distance between \(OP\) is \(1\) meter. The torque experienced by the magnetic dipole \(M_2\) due to the presence of \(M_1\) is:
1. \(3\times 10^{-7}~\text{N-m}\)
2. \(1\times 10^{-7}~\text{N-m}\)
3. \(4\times 10^{-7}~\text{N-m}\)
4. \(2\times 10^{-7}~\text{N-m}\)
1. \(3\times 10^{-7}~\text{N-m}\)
2. \(1\times 10^{-7}~\text{N-m}\)
3. \(4\times 10^{-7}~\text{N-m}\)
4. \(2\times 10^{-7}~\text{N-m}\)
Subtopic: Ā Magnetic Moment |
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A uniform conducting wire of length \(24a\) and resistance \({R}\) is wound up as a current-carrying coil in the shape of an equilateral triangle of side \({'a'}\) and then in the form of a square of side \({'a'}.\) The coil is connected to a voltage source \({V_0.}\) The ratio of the magnetic moment of the coils in case of an equilateral triangle to that for square is \({1: \sqrt{y}}~,\) where the value of \(y\) is:
1. \(3\)
2. \(1\)
3. \(4\)
4. \(2\)
1. \(3\)
2. \(1\)
3. \(4\)
4. \(2\)
Subtopic: Ā Magnetic Moment |
Level 4: Below 35%
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A circular coil has moment of inertia \(0.8~\text{kgm}^2\) around any diameter and is carrying current to produce a magnetic moment of \(20~\text{Am}^2\). The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of \(4~\text{T}\) is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by \(60^\circ\) will be:
1. \( 20~ \text{rad}\text{s}^{-1} \)
2. \( 20 \pi ~\text{rad} \text{s}^{-1} \)
3. \( 10 \pi ~\text{rad} \text{s}^{-1} \)
4. \( 10 ~\text{rad} \text{s}^{-1} \)
Subtopic: Ā Magnetic Moment |
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