Two identical long conducting wires \(\mathrm{AOB}\) and \(\mathrm{COD}\) are placed at a right angle to each other, with one above the other such that '\(O\)' is the common point for the two. The wires carry \(I_1\) and \(I_2\) currents, respectively. Point '\(P\)' is lying at a distance '\(d\)' from '\(O\)' along a direction perpendicular to the plane containing the wires. What will be the magnetic field at the point \(P\)?
1. | \(\dfrac{\mu_0}{2\pi d}\left(\dfrac{I_1}{I_2}\right )\) | 2. | \(\dfrac{\mu_0}{2\pi d}\left[I_1+I_2\right ]\) |
3. | \(\dfrac{\mu_0}{2\pi d}\left[I^2_1+I^2_2\right ]\) | 4. | \(\dfrac{\mu_0}{2\pi d}\sqrt{\left[I^2_1+I^2_2\right ]}\) |
1. | \(\frac{M a_0}{e} ~\text{west,}~ \frac{M a_0}{e v_0}~\text{up}\) |
2. | \(\frac{M a_0}{e} ~\text {west,} ~\frac{2 M a_0}{e v_0}~\text{down}\) |
3. | \(\frac{M a_0}{e} ~\text{east,} \frac{2 M a_0}{e v_0}~\text{up}\) |
4. | \(\frac{M a_0}{e} ~\text {east,} \frac{3 M a_0}{e v_0} ~\text {down}\) |
Two similar coils of radius \(R\) are lying concentrically with their planes at right angles to each other. The currents flowing in them are \(I\) and \(2I,\) respectively. What will be the resultant magnetic field induction at the centre?
1. | \(\sqrt{5} \mu_0I \over 2R\) | 2. | \({3} \mu_0I \over 2R\) |
3. | \( \mu_0I \over 2R\) | 4. | \( \mu_0I \over R\) |
1. | \(-F\) | 2. | \(F\) |
3. | \(2F\) | 4. | \(-2F\) |
1. | \(3 \overrightarrow{F}\) | 2. | \(- \overrightarrow{F}\) |
3. | \(-3 \overrightarrow{F}\) | 4. | \( \overrightarrow{F}\) |
1. | \(8\) N in \(-z\text-\)direction. |
2. | \(4\) N in the \(z\text-\)direction. |
3. | \(8\) N in the \(y\text-\)direction. |
4. | \(8\) N in the \(z\text-\)direction. |
A closed-loop \(PQRS\) carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments \(PS\), \(SR,\) and \(RQ\) are \(F_1, F_2~\text{and}~F_3\) respectively, and are in the plane of the paper and along the directions shown,
then which of the following forces acts on the segment \(QP\)?
1. \(F_{3} - F_{1} - F_{2}\)
2. \(\sqrt{\left(F_{3} - F_{1}\right)^{2} + F_{2}^{2}}\)
3. \(\sqrt{\left(F_{3} - F_{1}\right)^{2} - F_{2}^{2}}\)
4. \(F_{3} - F_{1} + F_{2}\)
A particle of mass \(m\), charge \(Q\), and kinetic energy \(T\) enters a transverse uniform magnetic field of induction \(\vec B\). What will be the kinetic energy of the particle after seconds?
1. | \(3~\text{T}\) | 2. | \(2~\text{T}\) |
3. | \(\text{T}\) | 4. | \(4~\text{T}\) |