Q. No.Consider six wires with the same current flowing through them as they enter or exit the page. Rank the magnetic field's line integral counterclockwise around each loop, going from most positive to most negative.
1. \(B>C>D>A\)
2. \(B>C=D>A\)
3. \(B>A>C=D\)
4. \(C>B=D>A\)
1. \(B>C>D>A\)
2. \(B>C=D>A\)
3. \(B>A>C=D\)
4. \(C>B=D>A\)
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. | \(0\) |
| 1. | resistance of \(19.92~ \text{k} \Omega\) parallel to the galvanometer |
| 2. | resistance of \(19.92~ \text{k} \Omega\) in series with the galvanometer |
| 3. | resistance of \(20 ~\Omega\) parallel to the galvanometer |
| 4. | resistance of \(20~ \Omega\) in series with the galvanometer |
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. | \(D\) |
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)
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. | \(\overrightarrow{d B}=\dfrac{\mu_0 \mathrm{I}(\overrightarrow{d l} \cdot \vec{r})}{4 \pi|\overrightarrow{\mathrm{r}}|^3}\) |
| 1. | \(\frac{120}{3}~\Omega \) | 2. | \(\frac{30}{7}~\Omega \) |
| 3. | \(\frac{170}{3}~\Omega \) | 4. | \(\frac{150}{7}~\Omega \) |
| 1. | \(B \over 2\) | 2. | \(2B\) |
| 3. | \(B \over 4\) | 4. | \(2B \over 3\) |
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. \(\mu_{0} i_{1} i_{2}\)
2. \(\dfrac{\mu_{0} i_{1} i_{2}}{\pi}\)
3. \(\dfrac{\mu_{0} i_{1} i_{2}}{2 \pi}\)
4. \(2 \mu_{0} i_{1} i_{2}\)
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