A wire carrying current \(I\) has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to \(X\)-axis while the semicircular portion of radius \(R\) is lying in the \(Y\text-Z\) plane. The magnetic field at point \(O\) is:

An electron moving in a circular orbit of radius \(r\) makes \(n\) rotations per second. The magnetic field produced at the centre has a magnitude:
1. \(\frac{\mu_0ne}{2\pi r}\)
2. zero
3. \(\frac{n^2e}{r}\)
4. \(\frac{\mu_0ne}{2r}\)

Two identical long conducting wires \(\mathrm{AOB}\) and \(\mathrm{COD}\) are placed at a right angle to each other, with one above the other such that '\(O\)' is the common point for the two. The wires carry \(I_1\) and \(I_2\) currents, respectively. Point '\(P\)' is lying at a distance '\(d\)' from '\(O\)' along a direction perpendicular to the plane containing the wires. What will be the magnetic field at the point \(P\)?
1. \(\frac{\mu_0}{2\pi d}\left(\frac{I_1}{I_2}\right )\)
2. \(\frac{\mu_0}{2\pi d}\left[I_1+I_2\right ]\)
3. \(\frac{\mu_0}{2\pi d}\left[I^2_1+I^2_2\right ]\)
4. \(\frac{\mu_0}{2\pi d}\sqrt{\left[I^2_1+I^2_2\right ]}\)

Two similar coils of radius \(R\) are lying concentrically with their planes at right angles to each other. The currents flowing in them are \(I\) and \(2I,\) respectively. What will be the resultant magnetic field induction at the centre?
1. \(\sqrt{5} \mu_0I \over 2R\)
2. \({3} \mu_0I \over 2R\)
3. \( \mu_0I \over 2R\)
4. \( \mu_0I \over R\)

Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency of f Hz. The magnitude of magnetic induction at the centre of the ring is:

1. $\frac{{\mathrm{\mu }}_0\mathrm{qf}}{2\mathrm{\pi R}}$

2. $\frac{{\mathrm{\mu }}_0\mathrm{qf}}{2\mathrm{R}}$

3. $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{fR}}$

4. $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{\pi fR}}$

A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane. If the current in the loop is I, then the resultant magnetic field due to the two semicircular parts at their common centre is:

1. $\frac{{\mu }_{0}i}{2R}$

2. $\frac{{\mu }_{0}i}{4R}$

3. $\frac{{\mu }_{0}i}{\sqrt{2}R}$

4. $\frac{{\mu }_{0}i}{2\sqrt{2}R}$

Two circular coils 1 and 2 are made from the same wire but the radius of the 1^st coil is twice that of the 2^nd coil. What is the ratio of the potential difference applied across them so that the magnetic field at their centres is the same?
1. 3
2. 4
3. 6
4. 2