Magnetic Field Due To Various Cases

Two circular coils and are made from the same wire but the radius of the ^st coil is twice that of the ^nd coil. What is the ratio of the potential difference applied across them so that the magnetic field at their centres is the same?
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A thin ring of radius metre has a charge C uniformly spread on it. The ring rotates about its axis with a constant frequency of revolutions/s. The value of magnetic induction in ${}^{}$ at the centre of the ring is:
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Two similar coils of radius are lying concentrically with their planes at right angles to each other. The currents flowing in them are and respectively. What will be the resultant magnetic field induction at the centre?

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An alternating electric field of frequency $\mathrm{\nu }$, is applied across the dees (radius=R) of a cyclotron that is being used to accelerate protons (mass=m). The operating magnetic field B, used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by:

1. $\mathrm{B}=\frac{\mathrm{m\nu }}{\mathrm{e}}$ $\mathrm{and}$ $\mathrm{K}=2{\mathrm{m\backslash pi}}^2{\mathrm{\nu }}^2{\mathrm{R}}^2$

2. $\mathrm{B}=\frac{2\mathrm{\backslash pi\; m\nu }}{\mathrm{e}}$ $\mathrm{and}$ $\mathrm{K}={\mathrm{m}}^2{\mathrm{\backslash pi\; \nu R}}^2$

3. $\mathrm{B}=\frac{2\mathrm{\backslash pi\; m\nu }}{\mathrm{e}}$ $\mathrm{and}$ $\mathrm{K}=2{\mathrm{m\backslash pi}}^2{\mathrm{\nu }}^2{\mathrm{R}}^2$

4. $\mathrm{B}=\frac{\mathrm{m\nu }}{\mathrm{e}}$ $\mathrm{and}$ $\mathrm{K}={\mathrm{m}}^2{\mathrm{\backslash pi\; \nu R}}^2$

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is . It is then bent into a circular coil of turns. The magnetic field at the centre of this coil of turns will be:
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A long solenoid of radius has turns per mm. If current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:

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A very long conducting wire is bent in a semi-circular shape from to as shown in the figure. The magnetic field at the point for steady current configuration is given by:

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A tightly wound turns coil of radius carries a current of . The magnitude of the magnetic field at the centre of the coil is: (Take permeability of free space as SI units):
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