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Which one of the following gives the value of the magnetic field according to Biot-Savart’s law?
| 1. | \(\dfrac{{i} \Delta {l} \sin (\theta)}{{r}^2} \) | 2. | \(\dfrac{\mu_0}{4 \pi} \dfrac{i \Delta {l} \sin (\theta)}{r} \) |
| 3. | \(\dfrac{\mu_0}{4 \pi} \dfrac{{i} \Delta{l} \sin (\theta)}{{r}^2} \) | 4. | \(\dfrac{\mu_0}{4 \pi} {i} \Delta {l} \sin (\theta)\) |
Subtopic: Biot-Savart Law |
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Level 1: 80%+
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An element \(\Delta l=\Delta x \hat{i}\) is placed at the origin and carries a large current of \(I=10~\text A\) (as shown in the figure). What is the magnetic field on the \(y\text-\)axis at a distance of \(0.5~\text m?\)
\((\text{Given}~\Delta x=1~\text{cm})\)
| 1. | \(6\times 10^{-8}~\text{T}\) | 2. | \(4\times 10^{-8}~\text{T}\) |
| 3. | \(5\times 10^{-8}~\text{T}\) | 4. | \(5.4\times 10^{-8}~\text{T}\) |
Subtopic: Biot-Savart Law |
81%
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A straight wire carrying a current of \(12~\text{A}\) is bent into a semi-circular arc of radius \(2.0~\text{cm}\) as shown in the figure. Considering the magnetic field \(B\) at the centre of the arc, what will be the magnetic field due to the straight segments?
| 1. | \(0\) | 2. | \(1.2\times 10^{-4}~\text{T}\) |
| 3. | \(2.1\times 10^{-4}~\text{T}\) | 4. | None of these |
Subtopic: Biot-Savart Law |
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Level 1: 80%+
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The resistances of three parts of a circular loop are as shown in the figure. What will be the magnetic field at the centre of \(O\)
(current enters at \(A\) and leaves at \(B\) and \(C\) as shown)?
| 1. | \(\dfrac{\mu_{0} I}{6 a}\) | 2. | \(\dfrac{\mu_{0} I}{3 a}\) |
| 3. | \(\dfrac{2\mu_{0} I}{3 a}\) | 4. | \(0\) |
Subtopic: Magnetic Field due to various cases |
82%
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Which of the following graphs correctly represents the variation of magnetic field induction with distance due to a thin wire carrying current?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Magnetic Field due to various cases |
80%
Level 1: 80%+
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What is the magnetic field at point \(O\) in the figure?
| 1. | \(\dfrac{\mu_{0} I}{4 \pi r}\) | 2. | \(\dfrac{\mu_{0} I}{4 \pi r} + \dfrac{\mu_{0} I}{2 \pi r}\) |
| 3. | \(\dfrac{\mu_{0} I}{4 r} + \dfrac{\mu_{0} I}{4 \pi r}\) | 4. | \(\dfrac{\mu_{0} I}{4 r} - \dfrac{\mu_{0} I}{4 \pi r}\) |
Subtopic: Magnetic Field due to various cases |
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Two identical long conducting wires \(({AOB})\) and \(({COD})\) are placed at a right angle to each other, with one above the other such that '\(O\)' is the common point for the two. The wires carry \(I_1\) and \(I_2\) currents, respectively. The point '\(P\)' is lying at a distance '\(d\)' from '\(O\)' along a direction perpendicular to the plane containing the wires. What will be the magnetic field at the point \(P?\)
| 1. | \(\dfrac{\mu_0}{2\pi d}\left(\dfrac{I_1}{I_2}\right )\) | 2. | \(\dfrac{\mu_0}{2\pi d}\left[I_1+I_2\right ]\) |
| 3. | \(\dfrac{\mu_0}{2\pi d}\left[I^2_1+I^2_2\right ]\) | 4. | \(\dfrac{\mu_0}{2\pi d}\sqrt{\left[I^2_1+I^2_2\right ]}\) |
Subtopic: Magnetic Field due to various cases |
77%
Level 2: 60%+
AIPMT - 2014
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If the magnetic field at the centre of the circular coil is \(B_0,\) then what is the distance on its axis from the centre of the coil where \(B_x=\frac{B_0}{8}?\)
(\(R\) = radius of the coil)
(\(R\) = radius of the coil)
| 1. | \(R \over 3\) | 2. | \(\sqrt{3}R\) |
| 3. | \(R \over \sqrt3\) | 4. | \(R \over 2\) |
Subtopic: Magnetic Field due to various cases |
74%
Level 2: 60%+
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A circular coil is in the \(y\text-z\) plane with its centre at the origin. The coil carries a constant current. Assuming the direction of the magnetic field at \(x= -25~\text{cm}\) to be positive, which of the following graphs shows the variation of the magnetic field along the \(x\text-\)axis?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Magnetic Field due to various cases |
72%
Level 2: 60%+
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A current loop consists of two identical semicircular parts each of radius \(R,\) one lying in the \(x\text-y\) plane, and the other in the \(x\text-z\) plane. If the current in the loop is \(i,\) what will be the resultant magnetic field due to the two semicircular parts at their common centre?
| 1. | \( \dfrac{\mu_0 i}{2 \sqrt{2} R} \) | 2. | \( \dfrac{\mu_0 i}{2 R} \) |
| 3. | \( \dfrac{\mu_0 i}{4 R} \) | 4. | \( \dfrac{\mu_0 i}{\sqrt{2} R}\) |
Subtopic: Magnetic Field due to various cases |
67%
Level 2: 60%+
NEET - 2010
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