An infinitely long straight conductor carries a current of \(5~\text{A}\) as shown. An electron is moving with a speed of \(10^5~\text{m/s}\) parallel to the conductor. The perpendicular distance between the electron and the conductor is \(20~\text{cm}\) at an instant. Calculate the magnitude of the force experienced by the electron at that instant.
1. \(4\pi\times 10^{-20}~\text{N}\)
2. \(8\times 10^{-20}~\text{N}\)
3. \(4\times 10^{-20}~\text{N}\)
4. \(8\pi\times 10^{-20}~\text{N}\)
A uniform conducting wire of length \(12a\) and resistance '\(R\)' is wound up as a current carrying coil in the shape of,
(i) | an equilateral triangle of side '\(a\)' |
(ii) | a square of side '\(a\)' |
The magnetic dipole moments of the coil in each case respectively are:
1. \(3Ia^2~\text{and}~4Ia^2\)
2. \(4Ia^2~\text{and}~3Ia^2\)
3. \(\sqrt{3}Ia^2~\text{and}~3Ia^2\)
4. \(3Ia^2~\text{and}~Ia^2\)
In the product
\(\vec{F}=q\left ( \vec{v}\times \vec{B} \right )\)
\(~~~=q\vec{v}\times \left ( B\hat{i}+B\hat{j}+B_0\hat{k} \right )\)
For \(q=1\) and \(\vec{v}=2\hat{i}+4\hat{j}+6\hat{k}\)
and \(\vec{F}=4\hat{i}-20\hat{j}+12\hat{k}\)
What will be the complete expression for \(\vec{B}\)?
1. \(8\hat{i}+8\hat{j}-6\hat{k}\)
2. \(6\hat{i}+6\hat{j}-8\hat{k}\)
3. \(-8\hat{i}-8\hat{j}-6\hat{k}\)
4. \(-6\hat{i}-6\hat{j}-8\hat{k}\)
A thick current-carrying cable of radius '\(R\)' carries current \('I'\) uniformly distributed across its cross-section. The variation of magnetic field \(B(r)\) due to the cable with the distance '\(r\)' from the axis of the cable is represented by:
1. | 2. | ||
3. | 4. |
1. | \(6.28 \times 10^{-4} ~\text{T} \) | 2. | \(6.28 \times 10^{-2}~\text{T}\) |
3. | \(12.56 \times 10^{-2}~\text{T}\) | 4. | \(12.56 \times 10^{-4} ~\text{T}\) |
Statement I: | Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element \(I(dl)\) of a current-carrying conductor only. |
Statement II: | Biot-Savart's law is analogous to Coulomb's inverse square law of charge \(q,\) with the former being related to the field produced by a scalar source, \(Idl\) while the latter being produced by a vector source, \(q.\) |
1. | Statement I is incorrect but Statement II is correct. |
2. | Both Statement I and Statement II are correct. |
3. | Both Statement I and Statement II are incorrect. |
4. | Statement I is correct but Statement II is incorrect. |
1. | a linearly decreasing function of distance upto the boundary of the wire and then a linearly increasing one for the outside region. |
2. | uniform and remains constant for both regions. |
3. | a linearly increasing function of distance upto the boundary of the wire and then a linearly decreasing one for the outside region. |
4. | a linearly increasing function of distance \(r\) upto the boundary of the wire and then decreasing one with \(1/r\) dependence for the outside region. |
The ratio of the radii of two circular coils is \(1:2\). The ratio of currents in the respective coils such that the same magnetic moment is produced at the centre of each coil is:
1. \(4:1\)
2. \(2:1\)
3. \(1:2\)
4. \(1:4\)
1. | a parabolic path |
2. | the original path |
3. | a helical path |
4. | a circular path |