Q. No.
| 1. | \(\frac{\mu_0 i}{4 R}\left[1-\frac{2}{\pi}\right]\) pointed into the page |
| 2. | \(\frac{\mu_0 i}{4 R}\) pointed into the page |
| 3. | \(\frac{\mu_0 i}{4 R}\) pointed away from the page |
| 4. | \(\frac{\mu_0 i}{4 R}\left[1-\frac{2}{\pi}\right]\) pointed away from the page |
| 1. | \(6.28 \times 10^{-4} ~\text{T} \) | 2. | \(6.28 \times 10^{-2}~\text{T}\) |
| 3. | \(12.56 \times 10^{-2}~\text{T}\) | 4. | \(12.56 \times 10^{-4} ~\text{T}\) |
(permeability of free space = \(4 \pi \times 10^{-7}~ \text{H/m}\))
| 1. | \(10^{-1}~\text{T}\) | 2. | \(10^{-2}~\text T\) |
| 3. | \(10^{2}~\text T\) | 4. | \(10^{-3}~\text{T}\) |
1. a straight line
2. circular
3. elliptical
4. a plane
1. \(3.14 \times 10^{-7} ~\text{T} \)
2. \(6.28 \times 10^{-7} ~\text{T} \)
3. \(3.14 \times 10^{-4} ~\text{T} \)
4. \(6.28 \times 10^{-4} ~\text{T}\)
A long solenoid of \(50~\text{cm}\) length having \(100\) turns carries a current of \(2.5~\text{A}\). The magnetic field at the centre of the solenoid is: \(\mu_0 = 4\pi\times 10^{-7}~\text{TmA}^{-1}\)
1. \(3.4\times 10^{-4}~\text{T}\)
2. \(6.28\times 10^{-5}~\text{T}\)
3. \(3.14\times 10^{-5}~\text{T}\)
4. \(6.28\times 10^{-4}~\text{T}\)
A straight conductor carrying current \(I\) splits into two parts as shown in the figure. The radius of the circular loop is \(R\). The total magnetic field at the centre \(P\) of the loop is:
| 1. | zero | 2. | \(\frac{3\mu_0 i}{32R},~\text{inward}\) |
| 3. | \(\frac{3\mu_0 i}{32R},~\text{outward}\) | 4. | \(\frac{\mu_0 i}{2R},~\text{inward}\) |
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. The magnetic field at the centre of this coil of \(n\) turns will be:
| 1. | \(nB\) | 2. | \(n^2B\) |
| 3. | \(2nB\) | 4. | \(2n^2B\) |
A wire carrying current \(I\) has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to \(X\)-axis while the semicircular portion of radius \(R\) is lying in the \(Y\text-Z\) plane. The magnetic field at point \(O\) is:
1. \(B=\frac{\mu i }{4\pi R}\left ( \pi \hat{i}+2\hat{k} \right )\)
2. \(B=-\frac{\mu i }{4\pi R}\left ( \pi \hat{i}-2\hat{k} \right )\)
3. \(B=-\frac{\mu i }{4\pi R}\left ( \pi \hat{i}+2\hat{k} \right )\)
4. \(B=\frac{\mu i }{4\pi R}\left ( \pi \hat{i}-2\hat{k} \right )\)
An electron moving in a circular orbit of radius \(r\) makes \(n\) rotations per second. The magnetic field produced at the centre has a magnitude:
1. \(\frac{\mu_0ne}{2\pi r}\)
2. zero
3. \(\frac{n^2e}{r}\)
4. \(\frac{\mu_0ne}{2r}\)
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