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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. | \(\frac{\mu_0}{4 \pi} {i} \Delta {l} \sin (\theta)\) |
Subtopic: Â Biot-Savart Law |
 89%
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To maximise the magnetic field caused by a small element of a current-carrying conductor at a point, the angle between the element and the line connecting the element to the point \(P\) must be:
| 1. | \(0^{\circ}\) | 2. | \(90^{\circ}\) |
| 3. | \(180^{\circ}\) | 4. | \(45^{\circ}\) |
Subtopic: Â Biot-Savart Law |
 87%
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An element \(\Delta l=\Delta x \hat{i}\) is placed at the origin and carries a large current of \(I=10\) A (as shown in the figure). What is the magnetic field on the \(y\text-\)axis at a distance of \(0.5\) m? (\(\Delta x=1~\text{cm}\))
| 1. | \(6\times 10^{-8}~\text{T}\) | 2. | \(4\times 10^{-8}~\text{T}\) |
| 3. | \(5\times 10^{-8}~\text{T}\) | 4. | \(5.4\times 10^{-8}~\text{T}\) |
Subtopic: Â Biot-Savart Law |
 80%
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A straight wire carrying a current of \(12\) A is bent into a semi-circular arc of radius \(2.0\) cm as shown in the figure. Considering the magnetic field \(B\) at the centre of the arc, what will be the magnetic field due to the straight segments?
1. \(0\)
2. \(1.2\times 10^{-4}~\text{T}\)
3. \(2.1\times 10^{-4}~\text{T}\)
4. None of these
Subtopic: Â Biot-Savart Law |
 78%
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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. | \(\overrightarrow{d B}=\frac{\mu_0 \mathrm{I}(\overrightarrow{d l} \cdot \vec{r})}{4 \pi|\overrightarrow{\mathrm{r}}|^3}\) |
Subtopic: Â Biot-Savart Law |
 68%
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