A bar magnet having a magnetic moment of \(2.0\times10^{5}~\text{JT}^{-1}\) is placed along the direction of the uniform magnetic field of magnitude, \(B=14\times10^{-5}~\text{T}\). The work done in rotating the magnet slowly through \(60^\circ \) from the direction of the field is:
1. \(14~\text{J}\)
2. \(8.4~\text{J}\)
3. \(4~\text{J}\)
4. \(1.4~\text{J}\)
Subtopic:  Bar Magnet |
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If a magnetic needle is made to vibrate in uniform field \(H\), then its time period is \(T\). If it vibrates in the field of intensity \(4H\), its time period will be:

1. \(2T\) 2. \(\dfrac{T}{2}\)
3. \(\dfrac{2}{T}\) 4. \(T\)
Subtopic:  Bar Magnet |
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A \(100\)-turn coil of wire of size \(2~\text{cm}\times 1.5~\text{cm}\) is suspended between the poles of a magnet producing a field of \(1~\text T,\)  inside a galvanometer. Calculate the torque on the coil due to a current of \(0.1~\text{A}\) passing through the coil.
1. \(3 \times 10^{-5}\) N-m 
2. \(30\) N-m
3. \(3 \times 10^{-3}\) N-m 
4. \(3 \times 10^{-2}\) N-m 
Subtopic:  Bar Magnet |
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A bar magnet of length \(l\) and magnetic dipole moment \(M\) is bent in the form of an arc as shown in the figure. The new magnetic dipole moment will be:

1. \(\dfrac{3M}{\pi}\) 2. \(\dfrac{2M}{l\pi}\)
3. \(\dfrac{M}{ 2}\) 4. \(M\)
Subtopic:  Bar Magnet |
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Due to a small magnet, the intensity at a distance \(x\) in the end-on position is \(9~\text{gauss}\). What will be the intensity at a distance \(\dfrac{x}{2}\) on equatorial position?
1. \(9~\text{gauss}\) 2. \(4~\text{gauss}\)
3. \(36~\text{gauss}\) 4. \(4.5~\text{gauss}\)
Subtopic:  Bar Magnet |
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A long magnetic needle of length \(2L\), magnetic moment \(M\) and pole strength \(m\) units is broken into two pieces at the middle. The magnetic moment and pole strength of each piece will be:
1. \(\frac{M}{2} , \frac{m}{2}\)
2. \(M , \frac{m}{2}\)
3. \(\frac{M}{2} , m\)
4. \(M, m\)

Subtopic:  Bar Magnet |
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A bar magnet of the magnetic moment \(M\) is placed at right angles to a magnetic induction \(B.\) If a force \(F\) is experienced by each pole of the magnet, the length of the magnet will be:
1. \(\frac{MB}{F}\) 2. \(\frac{BF}{M}\)
3. \(\frac{MF}{B}\) 4. \(\frac{F}{MB}\)
Subtopic:  Bar Magnet |
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The magnetic moment of a bar magnet of length \(L\) and area of cross-section \(A\) is \(M\). If the magnet is cut into four identical parts each of length \(L\) and area of cross-section \(\frac{A}{4}\), then magnetic moment of each part is:

1. \(\frac{M}{4}\) 2. \(\frac{M}{2}\)
3. \(M\) 4. \(4M\)
Subtopic:  Bar Magnet |
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The unit of pole strength is:
1. \(\text{Am}^2\)
2. \(\text{Am}\)
3. \(\frac{\text{A}^2}{\text{m}}\)
4. \(\frac{\text{A}^2}{\text{m}^2}\)

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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. \(\dfrac{\sqrt{5}\mu_{0} M}{4\pi d^{3}}\)
Subtopic:  Bar Magnet |
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