Moving Charges And Magnetism

The magnetic field at the centre of a current carrying loop of radius 0.1 m is $5\sqrt{5}$ times that at a point along its axis. The distance of this point from the centre of the loop is

• 0.1 m

• 0.2 m

• 0.05 m

• 0.25 m

A wire carrying currenti is shaped as shown. Section AB is a quarter circle of radius r. The magnetic field is directed

• perpendicular to the plane of the paper and directed into the paper

• at an angle $\frac{\mathrm{\pi }}{4}$to the plane of the paper

• along the bisector of the angle ACB away from AB

• along the bisector of ACB towards AB

The wire loop formed by joining two semicircular sections of radii R₁ and R₂ and centre C, carries a current I as shown. The magnetic field at C has a magnitude

• $\frac{{\mathrm{\mu }}_0\mathrm{I}}{2} \left(\frac{1}{{\mathrm{R}}_1} - \frac{1}{{\mathrm{R}}_2}\right)$

• $\frac{{\mathrm{\mu }}_0\mathrm{I}}{4} \left(\frac{1}{{\mathrm{R}}_1} - \frac{1}{{\mathrm{R}}_2}\right)$

• $\frac{{\mathrm{\mu }}_0\mathrm{I}}{2} \left(\frac{1}{{\mathrm{R}}_1} + \frac{1}{{\mathrm{R}}_2}\right)$

• $\frac{{\mathrm{\mu }}_0\mathrm{I}}{4} \left(\frac{1}{{\mathrm{R}}_1} + \frac{1}{{\mathrm{R}}_2}\right)$