Figure shows two small identical magnetic dipoles \(a\) and \(b\) of magnetic moments \(M\) each, placed at a separation \(2d\), with their axes perpendicular to each other. The magnetic field at the point \(P\) midway between the dipoles is:

         
 

1.	\(\dfrac{2 \mu_{0} M}{4 \pi d^{3}}\)	2.	\(\dfrac{\mu_{0} M}{4 \pi d^{3}}\)
3.	zero	4.	\(\dfrac{\sqrt{5}\mu_{0} M}{4\pi d^{3}}\)

A Rowland ring of mean radius \(15\) cm has \(3500\) turns of wire wound on a ferromagnetic core of relative permeability \(800.\) What is the magnetic field \(B\) in the core for a magnetizing current of \(1.2\) A?
1. \(3.27\) T
2. \(2.56\) T
3. \(1.05\) T
4. \(4.48\) T

A closely wound solenoid of \(800\) turns and area of cross-section \(2.5 \times10^{-4}~\text{m}^2\) carries a current of \(3.0~\text{A}\). If the solenoid acts like a bar magnet, then what is its associated magnetic moment?
1. \(0.6~\text{J/T}\) 
2. \(0.07~\text{J/T}\) 
3. \(0.3~\text{J/T}\) 
4. \(0.8~\text{J/T}\) 

A bar magnet of length \(l\) and magnetic moment \(p_{m}\)${\mathrm{}}_{}$ is bent in the form of an arc as shown in the figure below. The new magnetic dipole moment will be:

An iron rod of susceptibility \(599\) is subjected to a magnetizing field of \(1200~\text{A m}^{-1}.\) The permeability of the material of the rod is:
\((\mu_0 = 4 \pi\times 10^{-7}~\text{T mA}^{-1})\)
1. \(8.0\times 10^{-5}~\text{T mA}^{-1}\)
2. \(2.4\pi\times 10^{-5}~\text{T mA}^{-1}\)
3. \(2.4\pi\times 10^{-7}~\text{T mA}^{-1}\)
4. \(2.4\pi\times 10^{-4}~\text{T mA}^{-1}\)

A magnetic needle suspended parallel to a magnetic field requires \(\sqrt{3}~\text{J}\) of work to turn it through $\mathrm{}$\(60^\circ\). The torque needed to maintain the needle in this position will be:
1. \(3\) N-m
2. \(\sqrt{3} \) N-m
3. \(\frac32\) N-m
4. \(2\sqrt{3}\) N-m

If the magnetic dipole moment of an atom of diamagnetic material, paramagnetic material and ferromagnetic material are denoted by \(\mu_d,~\mu_p,~\text{and}~\mu_f\) respectively, then:
1. \(\mu_p= 0 ~\text{and}~\mu_f \ne0\)
2. \(\mu_d\neq 0 ~\text{and}~\mu_p=0\)
3. \(\mu_d\ne 0 ~\text{and}~\mu_f \ne0\)
4. \(\mu_d= 0 ~\text{and}~\mu_p \ne0\)

Which of the following is the correct representation of magnetic field lines?

A solenoid has a core of material with relative permeability \(400.\) The windings of the solenoid are insulated from the core and carry a current of \(2~\text A.\) If the number of turns is \(1000\) per metre, the magnetic field intensity \(H\) is:
1. \(2\times10^2~\text{A/m}\)
2. \(2\times10^3~\text{A/m}\)
3. \(2~\text{A/m}\) 
4. \(20~\text{A/m}\)

Choose the correct statement regarding magnetism.