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. |
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. \(-6\hat{i}-6\hat{j}-8\hat{k}\)
1. | the speed of the particle remains unchanged. |
2. | the direction of the particle remains unchanged. |
3. | the acceleration remains unchanged. |
4. | the velocity remains unchanged. |
A long solenoid carrying a current produces a magnetic field \(B\) along its axis.
If the current is doubled and the number of turns per cm is halved, what will be the new value of the magnetic field?
1. \(B/2\)
2. \(B\)
3. \(2B\)
4. \(4B\)
If the number of turns, area, and current through a coil are given by \(n\), \(A\) and \(i\) respectively then its magnetic moment will be:
1. \(niA\)
2. \(n^{2}iA\)
3. \(niA^{2}\)
4. \(\frac{ni}{\sqrt{A}}\)
The tangent galvanometer is used to measure:
1. Potential difference
2. Current
3. Resistance
4. In measuring the charge
In the Thomson mass spectrograph where \(\vec{E}\perp\vec{B}\) the velocity of the undeflected electron beam will be:
1. \(\frac{\left| \vec{E}\right|}{\left|\vec{B} \right|}\)
2. \(\vec{E}\times \vec{B}\)
3. \(\frac{\left| \vec{B}\right|}{\left|\vec{E} \right|}\)
4. \(\frac{E^{2}}{B^{2}}\)
An electron having mass 'm' and kinetic energy E enter in a uniform magnetic field B perpendicularly. Its frequency will be:
1.
2.
3.
4.