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Q. No.A \(100\text-\)turn closely wound circular coil of radius \(5~\text{cm}\) has a magnetic field of \(3.14 \times 10^{-3}~\text{T}\) at its centre. The current flowing through the coil, and the magnitude of the magnetic moment of this coil are, respectively:
(take \(\mu_0 = 4\pi \times 10^{-7}~\text{T-m/A}\))
1. \(2.5~\text{A}, 2~\text{A-m}^2\)
2. \(2.5~\text{A}, 20~\text{A-m}^2\)
3. \(2~\text{A},4~\text{A-m}^2\)
4. \(2~\text{A}, 10~\text{A-m}^2\)
(take \(\mu_0 = 4\pi \times 10^{-7}~\text{T-m/A}\))
1. \(2.5~\text{A}, 2~\text{A-m}^2\)
2. \(2.5~\text{A}, 20~\text{A-m}^2\)
3. \(2~\text{A},4~\text{A-m}^2\)
4. \(2~\text{A}, 10~\text{A-m}^2\)
Subtopic: Magnetic Moment |
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The figure given below shows a long, straight, solid wire of circular cross-section of radius \(a\) carrying a steady current \(I.\) The current \(I\) is uniformly distributed across its cross-section. The plot which correctly represents the variation of the magnetic field \((B)\) with distance \((r)\) from the axis of the conductor in the region is:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Ampere Circuital Law |
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A galvanometer of resistance \(100~\Omega\) gives full-scale deflection for a current of \(1\) mA. It is converted into an ammeter of range \(0\text-10\) A. The shunt required is:
1. \(0.01~\Omega\)
2. \(0.10~\Omega\)
3. \(0.001~\Omega\)
4. \(1.0~\Omega\)
1. \(0.01~\Omega\)
2. \(0.10~\Omega\)
3. \(0.001~\Omega\)
4. \(1.0~\Omega\)
Subtopic: Conversion to Ammeter & Voltmeter |
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A current \(I_0\) flows through a circular metallic loop of radius \(r\) as shown in the figure. The resistance of the segment \(ABC\) is half that of \(ADC.\)Magnitude of the magnetic field at the centre \(O\) of the loop is:
1. \(\dfrac{\mu_0 I_0}{2 \pi r}\)
2. \(\dfrac{\mu_0 I_0}{12 r}\)
3. \(\dfrac{\mu_0 I_0}{4 r}\)
4. \(\dfrac{\mu_0 I_0}{2 r}\)
1. \(\dfrac{\mu_0 I_0}{2 \pi r}\)
2. \(\dfrac{\mu_0 I_0}{12 r}\)
3. \(\dfrac{\mu_0 I_0}{4 r}\)
4. \(\dfrac{\mu_0 I_0}{2 r}\)
Subtopic: Magnetic Field due to various cases |
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Two infinitely long parallel conducting wires \(A\) and \(B\) carry currents \(I\) and \(2I,\) respectively, in the same direction. The wire \(A\) has a uniform mass per unit length \(\lambda\) and lies on an insulated floor. The wire \(B\) is kept fixed at a height \(h\) above the floor. The minimum magnitude of \(h\) so that the wire \(A\) does not rise from the floor is:
1. \( \dfrac{4\mu_0 I^2}{\pi \lambda g} \)
2. \( \dfrac{\mu_0 I^2}{2\pi \lambda g} \)
3. \( \dfrac{\mu_0 I^2}{\pi \lambda g} \)
4. \( \dfrac{2\mu_0 I^2}{\pi \lambda g} \)
1. \( \dfrac{4\mu_0 I^2}{\pi \lambda g} \)
2. \( \dfrac{\mu_0 I^2}{2\pi \lambda g} \)
3. \( \dfrac{\mu_0 I^2}{\pi \lambda g} \)
4. \( \dfrac{2\mu_0 I^2}{\pi \lambda g} \)
Subtopic: Force between Current Carrying Wires |
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A model for the quantized motion of an electron in a uniform magnetic field \(B\) states that the flux passing through the orbit of the electron is \(n(h/e)\) where \(n\) is an integer, \(h\) is Planck's constant and \(e\) is the magnitude of the electron's charge. According to the model, the magnetic moment of an electron is its lowest energy state will be (\(m\) is the mass of the electron):
| 1. | \(\dfrac{heB}{\pi m}\) | 2. | \(\dfrac{heB}{2\pi m}\) |
| 3. | \(\dfrac{he}{\pi m}\) | 4. | \(\dfrac{he}{2\pi m}\) |
Subtopic: Magnetic Moment |
Level 3: 35%-60%
NEET - 2025
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An electron (mass \(9\times10^{-31}~\text{kg}\) and charge \(1.6\times10^{-19}~\text C\)) moving with speed \(c/100\) (\(c\)=speed of light) is injected into a magnetic field \(\vec B\) of magnitude \(9\times10^{-4}~\text{T}\) perpendicular to its direction of motion. We wish to apply an uniform electric field \(\vec E\) together with the magnetic field so that the electron does not deflect from its path. Then (speed of light \(c=3\times10^8~\text{ms}^{-1}\))
| 1. | \(\vec E\) is parallel to \(\vec B\) and its magnitude is \(27\times10^{2}~\text{V m}^{-1}\) |
| 2. | \(\vec E\) is parallel to \(\vec B\) and its magnitude is \(27\times10^{4}~\text{V m}^{-1}\) |
| 3. | \(\vec E\) is perpendicular to \(\vec B\) and its magnitude is \(27\times10^{4}~\text{V m}^{-1}\) |
| 4. | \(\vec E\) is perpendicular to \(\vec B\) and its magnitude is \(27\times10^{2}~\text{V m}^{-1}\) |
Subtopic: Lorentz Force |
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A \(2~\text{amp}\) current is flowing through two different small circular copper coils having radii ratio \(1:2.\) The ratio of their respective magnetic moments will be:
| 1. | \(2: 1\) | 2. | \(4: 1\) |
| 3. | \(1: 4\) | 4. | \(1: 2\) |
Subtopic: Magnetic Moment |
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A tightly wound \(100\) turns coil of radius \(10~\text{cm}\) carries a current of \(7~\text A\). The magnitude of the magnetic field at the centre of the coil is: (Take permeability of free space as \(4 \pi \times 10^{-7}\)SI units):
1. \(4.4~\text T\)
2. \(4.4~\text {mT}\)
3. \(44~\text T\)
4. \(44~\text {mT}\)
1. \(4.4~\text T\)
2. \(4.4~\text {mT}\)
3. \(44~\text T\)
4. \(44~\text {mT}\)
Subtopic: Magnetic Field due to various cases |
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A wire carrying a current \(I\) along the positive \(x\)-axis has length \(L\). It is kept in a magnetic field \(\overrightarrow{B}=(2 \hat{i}+3 \hat{j}-4 \hat{k})~\text{T}\). The magnitude of the magnetic force acting on the wire is:
1. \(\sqrt{3}IL\)
2. \(3IL\)
3. \(\sqrt{5}IL\)
4. \(5IL\)
1. \(\sqrt{3}IL\)
2. \(3IL\)
3. \(\sqrt{5}IL\)
4. \(5IL\)
Subtopic: Lorentz Force |
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