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. | \(\frac{\mu_0}{4 \pi} {i} \Delta {l} \sin (\theta)\) |
1. | \(0^{\circ}\) | 2. | \(90^{\circ}\) |
3. | \(180^{\circ}\) | 4. | \(45^{\circ}\) |
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. | \(5.4\times 10^{-8}~\text{T}\) |
1. | \(0\) | 2. | \(1.2\times 10^{-4}~\text{T}\) |
3. | \(2.1\times 10^{-4}~\text{T}\) | 4. | None of these |
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. | \(\overrightarrow{d B}=\frac{\mu_0 \mathrm{I}(\overrightarrow{d l} \cdot \vec{r})}{4 \pi|\overrightarrow{\mathrm{r}}|^3}\) |