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 $\Omega$

A square current-carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is \( \overrightarrow{F}\), what will be the net force on the remaining three arms of the loop? 

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 F₁, F_2, and F₃ 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. ${\mathrm{F}}_3-{\mathrm{F}}_1-{\mathrm{F}}_2$

2. $\sqrt{{\left({\mathrm{F}}_3-{\mathrm{F}}_1\right)}^2+{\mathrm{F}}_2^2}$

3. $\sqrt{{\left({\mathrm{F}}_3-{\mathrm{F}}_1\right)}^2-{\mathrm{F}}_2^2}$

4. ${\mathrm{F}}_3-{\mathrm{F}}_1+{\mathrm{F}}_2$

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?

If a charged particle (charge q) is moving in a circle of radius R at a uniform speed v, then the value of its associated magnetic moment μ will be:

1. $\frac{\mathrm{qvR}}{2}$

2. ${\mathrm{qvR}}^2$

3. $\frac{{\mathrm{qvR}}^2}{2}$

4. $\mathrm{qvR}$