If a square loop \(\text{ABCD}\) carrying a current \(i\) is placed near and coplanar with a long straight conductor \(\mathrm{XY}\) carrying a current \(I\), what will be the net force on the loop?
1. \(\frac{\mu_0Ii}{2\pi}\)
2. \(\frac{2\mu_0IiL}{3\pi}\)
3. \(\frac{\mu_0IiL}{2\pi}\)
4. \(\frac{2\mu_0Ii}{3\pi}\)
Moving perpendicular to field \(B\), a proton and an alpha particle both enter an area of uniform magnetic field \(B\). If the kinetic energy of the proton is \(1~\text{MeV}\) and the radius of the circular orbits for both particles is equal, the energy of the alpha particle will be:
1. \(4~\text{MeV}\)
2. \(0.5~\text{MeV}\)
3. \(1.5~\text{MeV}\)
4. \(1~\text{MeV}\)
In an ammeter, \(0.2 \%\) of the main current passes through the galvanometer. If the resistance of the galvanometer is \(G,\) the resistance of the ammeter will be:
1. | \({1 \over 499}G\) | 2. | \({499 \over 500}G\) |
3. | \({1 \over 500}G\) | 4. | \({500 \over 499}G\) |
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. |