A current \(i\) flows through a semi-circular loop of radius \(r,\) attached to two long straight wires along the open diameter of the loop. The magnetic field at the centre of the loop is:
                              

1.  \(\frac{\mu_0i}{4r}\)
2.  \(\frac{\mu_0i}{4r}+\frac{\mu_0i}{2\pi r}\)
3.  \(\frac{\mu_0i}{4r}+\frac{\mu_0i}{4\pi r}\)
4.  \(\Big[\Big(\frac{\mu_0i}{4r}\Big)^2+\Big(\frac{\mu_0i}{4\pi r}\Big)^2\Big]^{\frac12}\)
Subtopic:  Magnetic Field due to various cases |
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The shape of the magnetic field lines due to an infinite long, straight current carrying conductor is:
1. a straight line
2. circular
3. elliptical
4. a plane
Subtopic:  Magnetic Field due to various cases |
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The magnetic field at a point (\(P\)) on the axis of a circular current carrying wire is \(\dfrac18\) of the field at its centre. The radius of the circular curve is \(R.\) The distance between \(P\) and the cente of the circle \((OP).\) is:
     
Then, 
1. \(OP=R\) 2. \(OP=\dfrac R2\)
3. \(OP=\sqrt3R\) 4. \(OP=8R\)
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Two long parallel wires carrying currents \(I_1\) and \(I_2\) give a magnetic field of \(3\) G at a point exactly mid-way between the two wires. When one of the currents is reversed, the field becomes \(5\) G. The ratio of the large current to the smaller one is:
1. \(2\) 2. \(\frac43\)
3. \(\frac32\) 4. \(4\)
Subtopic:  Magnetic Field due to various cases |
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A long solenoid of radius \(1~\text{mm}\) has \(100\) turns per mm. If \(1~\text{A}\) current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:
1. \(6.28 \times 10^{-4} ~\text{T} \) 2. \(6.28 \times 10^{-2}~\text{T}\)
3. \(12.56 \times 10^{-2}~\text{T}\) 4. \(12.56 \times 10^{-4} ~\text{T}\)
Subtopic:  Magnetic Field due to various cases |
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A long solenoid has a square cross-section of side \(a\). It has turn-density n (number of turns per unit axial length). A current \(i\) is passed through this solenoid. The magnetic field at the centre of the solenoid is \(B_c\). Then, \(B_c\) is proportional to:
(I) \(a\)
(II) \(1\over a\)
(III) \(n\)
(IV) \(i\)
1. I, III, IV 
2. II, III, IV 
3. III, IV
4. IV Only 
Subtopic:  Magnetic Field due to various cases |
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