Which one of the following gives the value of the magnetic field according to Biot-Savart’s law?

1. \(\frac{\mathrm{i} \Delta \mathrm{l} \sin (\theta)}{\mathrm{r}^2} \) 2. \(\frac{\mu_0}{4 \pi} \frac{\mathrm{i} \Delta \mathrm{l} \sin (\theta)}{\mathrm{r}} \)
3. \(\frac{\mu_0}{4 \pi} \frac{\mathrm{i} \Delta \mathrm{l} \sin (\theta)}{\mathrm{r}^2} \) 4. \(\frac{\mu_0}{4 \pi} \mathrm{i} \Delta \mathrm{l} \sin (\theta)\)
Subtopic:  Biot-Savart Law |
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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. 2. 90º
3. 180º 4. 45º
Subtopic:  Biot-Savart Law |
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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-axis at a distance of \(0.5\) m?(\(\Delta x=1~\mathrm{cm}\))
       

 1. \(6\times 10^{-8}~\mathrm{T}\) 2. \(4\times 10^{-8}~\mathrm{T}\)
3. \(5\times 10^{-8}~\mathrm{T}\) 4. \(5.4\times 10^{-8}~\mathrm{T}\)

Subtopic:  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. 1.2×10-4 T
3. 2.1×10-4 T
4. None of these

Subtopic:  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:  Biot-Savart Law |
 68%
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