The magnitude of the integral of the quantity \(\int\vec B\cdot d\vec{ l}\) around the loop \(PQR\) of the equilateral triangle is \(K.\) The field at the centre of the long solenoid is:
              
1. \(\dfrac{K}{a}\) 2. \(\dfrac{K}{b}\)
3. \(\dfrac{K}{a-b}\) 4. \(\dfrac{K}{a+b}\)

Subtopic:  Ampere Circuital Law |
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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. \(\dfrac{\mu_0i}{4r}\)
2. \(\dfrac{\mu_0i}{4r}+\dfrac{\mu_0i}{2\pi r}\)
3. \(\dfrac{\mu_0i}{4r}+\dfrac{\mu_0i}{4\pi r}\)
4. \(\left[\left(\dfrac{\mu_0i}{4r}\right)^2+\left(\dfrac{\mu_0i}{4\pi r}\right)^2\right]^{\frac12} \)
Subtopic:  Magnetic Field due to various cases |
 84%
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A long thin wire of length \(L\) carrying a current \(i,\) is wrapped uniformly around a long solenoid of volume \(V.\) The radius of the solenoid is \(r.\) The magnetic field at its centre is:
1. \(\dfrac{\mu_0~L~r~i}{V}\) 2. \(\dfrac{\mu_0~L~r~i}{2\pi~V}\)
3. \(\dfrac{\mu_0~L~r~i}{2V}\) 4. \(\dfrac{\mu_0~L~r~i}{4\pi~V}\)
Subtopic:  Magnetic Field due to various cases |
 51%
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A long cylindrical solenoid of length \(L\) and total number of turns \(N\) produces a magnetic field \(B_0\) at its centre with a current of \(1\) A flowing through its coils. If the same current of \(1\) A is sent through a circular wire of radius \(R\) then the same field \(B_0\) is produced at its centre. Then, \(\dfrac{R}{L}\) equals:
1. \(N\) 2. \(\dfrac 1N\)
3. \(2N\) 4. \(\dfrac{1}{2N}\)
Subtopic:  Magnetic Field due to various cases |
 74%
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A charged particle moves in a circular path of radius \(r\) in a uniform magnetic field \(B,\) perpendicular to the plane of motion. The same particle is observed to move in a circular path around an infinite line charge \(\lambda\) (charge/unit length), moving with the same kinetic energy as before. The charge to mass ratio of the particle is proportional to:
1. \(\lambda Br\) 2. \(\dfrac{\lambda Br}{r}\)
3. \(\dfrac{\lambda}{Br}\) 4. \(\dfrac{\lambda}{B^2r^2}\)
Subtopic:  Lorentz Force |
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A charged particle of charge \(q,\) mass \(m\) moves in a circular path under the action of a uniform magnetic field, whose flux through this path is \(\phi.\) The magnetic moment due to the particle's motion is:
1. \(\dfrac{q^2\phi}{2m}\) 2. \(\dfrac{q^2\phi}{2\pi m}\)
3. \(\dfrac{q^2\phi}{m}\) 4. \(\dfrac{q^2\phi}{\pi m}\)
Subtopic:  Magnetic Moment |
 71%
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A current-carrying wire is placed in a uniform magnetic field and the force on the wire is measured at different angular positions of the wire, as it is rotated in the \(x-y\) plane. Initially, the wire is along the \(x\)-axis. The magnitude of the magnetic force\((F)\) is plotted as a function of the angle\((\theta)\) made by the current-carrying wire with the \(x\)-axis.

Which of the following is the possible magnetic field (in tesla)?
1. \(2\hat j\)
2. \(2\hat k\)
3. \(2\hat i+2\hat k\)
4. \(2\hat j+2\hat k\)
Subtopic:  Magnetic Field due to various cases |
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A long straight current-carrying wire is placed along the axis of a solenoid and it is found that the field within the solenoid at a distance of \(\dfrac r{10}\) from the wire is doubled when a current \(I\) passes through the wire and the solenoid, \(r\) being the radius of the solenoid. The number of turns per unit length of the solenoid are:
1. \(\dfrac{5}{\sqrt3r}\) 2. \(\dfrac{5}{\sqrt3\pi r}\)
3. \(\dfrac{5}{r}\) 4. \(\dfrac{5}{\pi r}\)
Subtopic:  Magnetic Field due to various cases |
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An ammeter having a resistance of \(0.1~ \Omega\) can measure a maximum current of \(2~\text{A}\). To convert it into a voltmeter that can measure upto \(50~\text{V},\) one must add:
1. a resistance of \(25~\Omega\) in series
2. a resistance of \(\dfrac1{25}~\Omega\) in series
3. a resistance of \(25~\Omega\) in parallel
4. a resistance of \(\dfrac1{25}~\Omega\) in parallel
Subtopic:  Conversion to Ammeter & Voltmeter |
 74%
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A charged particle (charge: \(q\)) moves in a circular orbit in a uniform magnetic field, its orbit enclosing a magnetic flux \(\Phi.\) The angular momentum of the particle is:
 
1. \(q\Phi\) 2. \(\dfrac{q\Phi}{2\pi}\)
3. \(\pi q\Phi\) 4. \(\dfrac{q\Phi}{\pi}\)
Subtopic:  Lorentz Force |
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