An element \(\Delta l=\Delta x \hat{i}\) is placed at the origin and carries a large current of \(I=10~\text A\) (as shown in the figure). What is the magnetic field on the \(y\text-\)axis at a distance of \(0.5~\text m?\) 
\((\text{Given}~\Delta x=1~\text{cm})\)

1.	\(6\times 10^{-8}~\text{T}\)	2.	\(4\times 10^{-8}~\text{T}\)
3.	\(5\times 10^{-8}~\text{T}\)	4.	\(5.4\times 10^{-8}~\text{T}\)

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. \(4B\)

The resistances of three parts of a circular loop are as shown in the figure. What will be the magnetic field at the centre of \(O\) 
(current enters at \(A\) and leaves at \(B\) and \(C\) as shown)?

A neutron, a proton, an electron and an \(\alpha\text-\)particle enter a region of the uniform magnetic field with the same velocity. The magnetic field is perpendicular and directed into the plane of the paper. The tracks of the particles are labelled in the figure. Which track will the \(\alpha\text-\)particle follow?
              

A charged particle is projected through a region in a gravity-free space. If it passes through the region with constant speed, then the region may have:
1. \(\vec{E}=0, \vec{B} \neq 0\)
2. \(\vec{E} \neq 0, \vec{B} \neq 0\)
3. \(\vec{E} \neq 0, \vec{B}=0\)
4. Both (1) & (2)

If a long hollow copper pipe carries a direct current along its length, then the magnetic field associated with the current will be:

                
1. \(\mu_{0} i_{1} i_{2}\)
2. \(\dfrac{\mu_{0} i_{1} i_{2}}{\pi}\)
3. \(\dfrac{\mu_{0} i_{1} i_{2}}{2 \pi}\)
4. \(2 \mu_{0} i_{1} i_{2}\) 

What is the magnetic moment of the following current loop?
            
1. \(24~\text{Am}^2\)
2. \(12~\text{Am}^2\)
3. \(6~\text{Am}^2\)
4. zero