Q. No.What is the magnetic moment of the following current loop?
1. \(24~\text{Am}^2\)
2. \(12~\text{Am}^2\)
3. \(6~\text{Am}^2\)
4. zero
1. \(24~\text{Am}^2\)
2. \(12~\text{Am}^2\)
3. \(6~\text{Am}^2\)
4. zero
An electron and a proton are revolving around a common centre \(O\) in two coplanar circular paths as shown in the figure with a time period of rotation of \(1\) s and \(2\) s, respectively. What will be the net magnetic field at \(O\)?
| 1. | \(\frac{\mu _{0}e}{\pi }\) tesla | 2. | \(\frac{\mu _{0}e}{2}\) tesla |
| 3. | \(2\mu _{0}e\) tesla | 4. | zero |
1. \(\mu_{0} i_{1} i_{2}\)
2. \(\dfrac{\mu_{0} i_{1} i_{2}}{\pi}\)
3. \(\dfrac{\mu_{0} i_{1} i_{2}}{2 \pi}\)
4. \(2 \mu_{0} i_{1} i_{2}\)
If a long hollow copper pipe carries a direct current along its length, then the magnetic field associated with the current will be:
| 1. | only inside the pipe | 2. | only outside the pipe |
| 3. | both inside and outside the pipe | 4. | zero everywhere |
| 1. | \(B \over 2\) | 2. | \(2B\) |
| 3. | \(B \over 4\) | 4. | \(2B \over 3\) |
| 1. | \(\frac{120}{3}~\Omega \) | 2. | \(\frac{30}{7}~\Omega \) |
| 3. | \(\frac{170}{3}~\Omega \) | 4. | \(\frac{150}{7}~\Omega \) |
Which one of the following expressions represents Biot-Savart's law? Symbols have their usual meanings.
| 1. | \(\overrightarrow{d B}=\dfrac{\mu_0 \mathrm{I}(\overrightarrow{d l} \times \hat r)}{4 \pi|\overrightarrow{\mathrm{r}}|^3}\\ \) | 2. | \(\overrightarrow{d B}=\dfrac{\mu_0 \mathrm{I}(\overrightarrow{d l} \times \hat r)}{4 \pi|\overrightarrow{\mathrm{r}}|^2} \) |
| 3. | \(\overrightarrow{d B}=\dfrac{\mu_0 \mathrm{I}(\overrightarrow{d l} \times \vec{r})}{4 \pi|\vec{r}|^3} \) | 4. | \(\overrightarrow{d B}=\dfrac{\mu_0 \mathrm{I}(\overrightarrow{d l} \cdot \vec{r})}{4 \pi|\overrightarrow{\mathrm{r}}|^3}\) |
A charged particle is projected through a region in a gravity-free space. If it passes through the region with constant speed, then the region may have:
1. \(\vec{E}=0, \vec{B} \neq 0\)
2. \(\vec{E} \neq 0, \vec{B} \neq 0\)
3. \(\vec{E} \neq 0, \vec{B}=0\)
4. Both (1) & (2)
A neutron, a proton, an electron and an \(\alpha\text-\)particle enter a region of the uniform magnetic field with the same velocity. The magnetic field is perpendicular and directed into the plane of the paper. The tracks of the particles are labelled in the figure.
Which track will the \(\alpha\text-\)particle follow?
| 1. | \(A\) | 2. | \(B\) |
| 3. | \(C\) | 4. | \(D\) |
The two parts of the loop are circles of radii \(2a\) and \(a,\) respectively, and carry the same current \(i\) as shown in the given figure. What is the magnitude of the dipole moment of the current loop?
1. \(5 \pi a^{2}\hat i\)
2. \(4 \pi a^{2}\hat i\)
3. \(3 \pi a^{2}\hat i\)
4. zero
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