A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is \(B\). It is then bent into a circular coil of \(n\) turns. What will the magnetic field be at the centre of this \(n\text-\)turn coil?
1. \(nB\) 2. \(n^2B\)
3. \(2nB\) 4. \(2n^2B\)
Subtopic:  Magnetic Field due to various cases |
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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 |
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The magnetic induction at point \(P\), which is \(4\) cm from a long current-carrying wire is \(10^{-8}\) Tesla. What would be the field of induction at a distance of \(12\) cm from the same current?
1. \(3.33\times 10^{-9}\) Tesla   
2. \(1.11\times 10^{-4}\) Tesla
3. \(3\times 10^{-3}\) Tesla
4. \(9\times 10^{-2}\) Tesla
Subtopic:  Magnetic Field due to various cases |
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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 |
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Two similar coils of radius \(R\) are lying concentrically with their planes at right angles to each other. The currents flowing in them are \(I\) and \(2I,\) respectively. What will be the resultant magnetic field induction at the centre?

1. \(\sqrt{5} \mu_0I \over 2R\) 2. \({3} \mu_0I \over 2R\)
3. \( \mu_0I \over 2R\) 4. \( \mu_0I \over R\)
Subtopic:  Magnetic Field due to various cases |
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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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In the figure shown below there are two semicircles of radius \(r_1\) and \(r_2\) in which a current \(i\) is flowing. The magnetic induction at the centre of \(O\) will be:


 

1. \(\dfrac{\mu_{0} i}{r} \left(r_{1} + r_{2}\right)\) 2. \(\dfrac{\mu_{0} i}{4} \left[\frac{r_{1} + r_{2}}{r_{1} r_{2}}\right]\)
3. \(\dfrac{\mu_{0} i}{4} \left(r_{1} - r_{2}\right)\) 4. \(\dfrac{\mu_{0} i}{4} \left[\frac{r_{2} - r_{1}}{r_{1} r_{2}}\right]\)
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Two identical long conducting wires \(\mathrm{AOB}\) and \(\mathrm{COD}\) 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. 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 |
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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)
1. \(R \over 3\) 2. \(\sqrt{3}R\)
3. \(R \over \sqrt3\) 4. \(R \over 2\)
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A ring of radius \(R\) carries a linear charge density \(\lambda\). It is rotating with angular speed \(\omega\) about an axis passing through the centre and perpendicular to the plane. What is the magnetic field at its centre?

1. \(\dfrac{3 \mu_{0} \lambda \omega}{2}\) 2. \(\dfrac{\mu_{0} \lambda \omega}{2}\)
3. \(\dfrac{\mu_{0} \lambda \omega}{\pi}\) 4. \(\mu_{0} \lambda \omega\)
Subtopic:  Magnetic Field due to various cases |
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