Q. No.Which one of the following gives the value of the magnetic field according to Biot-Savart’s law?
| 1. | \(\frac{{i} \Delta {l} \sin (\theta)}{{r}^2} \) | 2. | \(\frac{\mu_0}{4 \pi} \frac{i \Delta {l} \sin (\theta)}{r} \) |
| 3. | \(\frac{\mu_0}{4 \pi} \frac{{i} \Delta{l} \sin (\theta)}{{r}^2} \) | 4. | \(\frac{\mu_0}{4 \pi} {i} \Delta {l} \sin (\theta)\) |
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| 1. | \(0^{\circ}\) | 2. | \(90^{\circ}\) |
| 3. | \(180^{\circ}\) | 4. | \(45^{\circ}\) |
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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. | \(5.4\times 10^{-8}~\text{T}\) |
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| 1. | \(0\) | 2. | \(1.2\times 10^{-4}~\text{T}\) |
| 3. | \(2.1\times 10^{-4}~\text{T}\) | 4. | None of these |
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Which one of the following expressions represents Biot-Savart's law? Symbols have their usual meanings.
| 1. | \(\overrightarrow{d B}=\frac{\mu_0 \mathrm{I}(\overrightarrow{d l} \times \hat r)}{4 \pi|\overrightarrow{\mathrm{r}}|^3}\\ \) | 2. | \(\overrightarrow{d B}=\frac{\mu_0 \mathrm{I}(\overrightarrow{d l} \times \hat r)}{4 \pi|\overrightarrow{\mathrm{r}}|^2} \) |
| 3. | \(\overrightarrow{d B}=\frac{\mu_0 \mathrm{I}(\overrightarrow{d l} \times \vec{r})}{4 \pi|\vec{r}|^3} \) | 4. | \(\overrightarrow{d B}=\frac{\mu_0 \mathrm{I}(\overrightarrow{d l} \cdot \vec{r})}{4 \pi|\overrightarrow{\mathrm{r}}|^3}\) |
| 1. | \(nB\) | 2. | \(n^2B\) |
| 3. | \(2nB\) | 4. | \(2n^2B\) |
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| 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 |
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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. | \( \mu_0I \over R\) |
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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. | \(0\) |
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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. |  |
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