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Q. No.A wire carrying a current \(i\) is bent into the form of an arc of a circle with center \(O\), joined smoothly to two long, straight wires at its ends. The magnetic field at the centre \(O\) is twice that due to the straight portions. The angle subtended at the centre \(O\) by the arc is:
1.
\(\theta=\dfrac{\pi}{3}\)
2.
\(\theta=\dfrac{\pi}{2}\)
3.
\(\theta=1\) rad
4.
\(\theta=2\) rad
Subtopic: Magnetic Field due to various cases |
62%
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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,
Then,
| 1. | \(OP=R\) | 2. | \(OP=\dfrac R2\) |
| 3. | \(OP=\sqrt3R\) | 4. | \(OP=8R\) |
Subtopic: Magnetic Field due to various cases |
76%
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The magnetic field at the center \(O\) of the semi-circular part of the current-carrying wire, due to the curved and the straight wires (very long), is:
| 1. | \({\Large\frac{\mu_0i}{4R}}\) |
| 2. | \({\Large\frac{\mu_0i}{4R}}+{\Large\frac{\mu_0i}{2\pi R}}\) |
| 3. | \({\Large\Big(\frac{\mu_0i}{4R}+\frac{\mu_0i}{4\pi R}\Big)} \) |
| 4. | \({\Large\Big[\Big(\frac{\mu_0i}{4R}\Big)^2+\Big(\frac{\mu_0i}{2\pi R}\Big)^2\Big]^{1/2}} \) |
Subtopic: Magnetic Field due to various cases |
67%
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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. \(2\hat j+2\hat k\)
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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