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. | \(\frac{\mu_0}{4 \pi} \mathrm{i} \Delta \mathrm{l} \sin (\theta)\) |
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. | 0º | 2. | 90º |
3. | 180º | 4. | 45º |
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. | \(5.4\times 10^{-8}~\mathrm{T}\) |
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?
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. | \(\overrightarrow{d B}=\frac{\mu_0 \mathrm{I}(\overrightarrow{d l} \cdot \vec{r})}{4 \pi|\overrightarrow{\mathrm{r}}|^3}\) |