A circular current carrying coil has a radius R. The distance from the centre of the coil, on the axis, where B will be  $\frac{1}{8}$  of its value at the centre of the coil is

• $\frac{\mathrm{R}}{\sqrt{3}}$

• $\sqrt{3} \mathrm{R}$

• 2 $\sqrt{3}$ R

• $\frac{2 \mathrm{R}}{\sqrt{3}}$

A current carrying loop is placed in a uniform magnetic field in four different orientations I, II, III and IV as shown in figure. Arrange them in decreasing order of potential energy

• l > lll> ll > lV

• l > ll > lll > lV

• l > lV > ll > lll

• lll > lV > l > ll

A current I is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure. The magnetic field at the centre of the loop is μ₀I/R times ( MA = R, MB = 2R, ∠DMA = 90^o )

• 5/16, but out of the plane of the paper.

• 5/16, but into the plane of the paper.

• 7/16, but out of the plane of the paper.

• 7/16, but into the plane of the paper.

Assertion:  Acceleration of charged particle in non-uniform electric field does not depend on velocity of charged particle.

Reason: Charge is an invariant quantity. That is amount of charge on particle does not depend on frame of reference.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

The magnetic field at the centre O of the arc shown in the figure is

• 2$\mathrm{I} \left( \sqrt{2} + \mathrm{\pi } \right) \times \frac{{10}^{-7}}{\mathrm{r}}$

• 2$\mathrm{I} \left(\sqrt{2} + \frac{\mathrm{\pi }}{4}\right) \times \frac{{10}^{-7}}{\mathrm{r}}$

• $\mathrm{I} \left(\sqrt{2} + \mathrm{\pi }\right)\times \frac{{10}^{-7}}{\mathrm{r}}$

• $\mathrm{I} \left(\sqrt{2} + \frac{\mathrm{\pi }}{4}\right) \times \frac{{10}^{-7}}{\mathrm{r}}$

Assertion:  Magnetic field is useful in producing parallel beam of charged particle. 

Reason:  Magnetic field inhibits the motion of
charged particle moving across it.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

What is the magnetic field on the axis of a coil of radius r carrying current I at a distance R from the origin?

• $\frac{{\mathrm{\mu }}_0 \mathrm{I} {\mathrm{r}}^2}{2 {\left({\mathrm{r}}^2 + {\mathrm{R}}^2\right)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

• $\frac{{\mathrm{\mu }}_0 {\mathrm{IR}}^2}{2 {\left({\mathrm{r}}^2 + {\mathrm{R}}^2\right)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

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

• $\frac{{\mathrm{\mu }}_0 \mathrm{IR}}{2 {\left({\mathrm{r}}^2 + {\mathrm{R}}^2\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

Assertion:  When a magnetic dipole is placed in a non uniform magnetic field, only a torque acts on the dipole. 

Reason:  Force would act on dipole if magnetic field is uniform.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false.

• If both assertion and reason are false.

Two parallel long wires A and B carry currents i₁ and i₂ ( < i₂ ). When i₁ and i₂ are in the same direction, the magnetic field at a point mid way between the wires is 10 µT. If i₂ is reverse the field becomes 30 µT. The ratio i₁ / i₂

• 1

• 2

• 3

• 4

Two conducting circular loops of radii R₁ and R₂ are placed in the same plane with their centres coinciding. If R₁ > R₂, the mutual inductance M between them will be directly proportional to

• $\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}$

• $\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}$

• $\frac{{\mathrm{R}}_1^{ 2}}{{\mathrm{R}}_2}$

• $\frac{{\mathrm{R}}_2^{ 2}}{{\mathrm{R}}_1^{ 2}}$