Circular  loop  of  a  wire  and a  long  straight  wire  carry currents  I_c  and  I_e respectively  as shown in figure. Assuming  that  these  are  places  in  the same plane, the magnetic  field  will be  zero  at  the  centre of  the loop when separation  H is

• $\frac{{\mathrm{I}}_{\mathrm{e}} \mathrm{R}}{{\mathrm{I}}_{\mathrm{c}} \mathrm{\pi }}$

• $\frac{{\mathrm{I}}_{\mathrm{c}} \mathrm{R}}{{\mathrm{I}}_{\mathrm{e} }\mathrm{\pi }}$

• $\frac{\mathrm{\pi } {\mathrm{I}}_{\mathrm{c}}}{{\mathrm{I}}_{\mathrm{e}} \mathrm{R}}$

• $\frac{{\mathrm{I}}_{\mathrm{e}} \mathrm{\pi }}{{\mathrm{I}}_{\mathrm{c}} \mathrm{R}}$

A metallic ring is dropped down, keeping its plane perpendicular to a constant and horizontal magnetic field. The ring enters the region of magnetic field at I = 0 and completely emerges out at  t = T sec. The current in the ring varies as

A conducting ring of radius 1 meter is placed in a uniform magnetic field B of 0.01 tesla oscillating with frequency 100 Hz with its plane at right angle to B. What will be the induced electric field?

• $\mathrm{\pi }$ volts/m

• 2 volts/m

• 10 volts/m

• 62 volts/m

94.

A proton and an  $\mathrm{\alpha }$ -particle, moving with the same velocity, enter into a uniform magnetic field, acting normal to the plane of their motion. The ratio of the radii of the circular paths described by the proton $\mathrm{\alpha }$-particle is

• 1 : 2

• 1 : 4

• 1 : 16

• 4 : 1

The electric field due to a uniformly charged sphere of radius R as a function of the distance from its centre is represented graphically by

A circular coil of radius is R carries an electric current. The magnetic field due to the coil at a point on the axis of the coil located at a point on the axis of the coil located at a distance r from the centre of the coil, such that r >> R, varies as 

• $\frac{1}{\mathrm{r}}$

• $\frac{1}{{\mathrm{r}}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

• $\frac{1}{{\mathrm{r}}^{ 2}}$

• $\frac{1}{{\mathrm{r}}^3}$

The magnetic field due to straight conductor of uniform cross-section of radius  ' a '  and carrying a steady current is represented by

The magnetic moment of a current (I) carrying circular coil of radius (r) and number of turns (n) varies as

• $\frac{1}{{\mathrm{r}}^2}$

• $\frac{1}{\mathrm{r}}$

• r

• r²

The cyclotron frequency of an electron  gyrating in a magnetic field of  1 T approximately

• 28 MHz

• 280 MHz

• 2.8 GHz

• 28 GHz

An electric dipole placed in a non-uniform electric field experiences

• both a torque and a net force

• only a force but no torque

• only a torque but no net force

• no torque and no net force