An arrangement of three parallel straight wires placed perpendicular to the plane of paper carrying the same current in the same direction is shown in the figure. The magnitude of force per unit length on the middle wire \(B\) is given by:
    

1.	\(\frac{\mu_0i^2}{2\pi d}\)	2.	\(\frac{2\mu_0i^2}{\pi d}\)
3.	\(\frac{\sqrt{2}\mu_0i^2}{\pi d}\)	4.	\(\frac{\mu_0i^2}{\sqrt{2}\pi d}\)

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:

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. \(\frac{\mu_0}{2\pi d}\left(\frac{I_1}{I_2}\right )\)
2. \(\frac{\mu_0}{2\pi d}\left[I_1+I_2\right ]\)
3. \(\frac{\mu_0}{2\pi d}\left[I^2_1+I^2_2\right ]\)
4. \(\frac{\mu_0}{2\pi d}\sqrt{\left[I^2_1+I^2_2\right ]}\)

When a proton is released from rest in a room, it starts with an initial acceleration \(a_0\) towards the east. When it is projected towards the north with a speed of \(v_0\), it moves with an initial acceleration of \(3a_0\) towards the east. What are the electric and magnetic fields in the room?

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. \( \mu_0I \over R\)

A current-carrying closed loop in the form of a right isosceles triangle ABC is placed in a uniform magnetic field acting along with AB.  If the magnetic force on the arm BC is F, then what is the force on the arm AC?
                

A galvanometer has a coil resistance of 100 Ω and gives a full-scale deflection for 30 mA of current. If it is to work as a voltmeter in the 30 V range, how much resistance does it require to be added?

1. 900 $\Omega$

2. 1800 $\Omega$

3. 500 $\Omega$

4. 1000 $\Omega$