Force between two identical charges placed at a distance of r in vacuum is F. Now a slab of dielectric of dielectric constant 4 is inserted  between these two charges. If the thickness of the slab is r/2, then the force between the charges will become

• F

• $\frac{3}{5} \mathrm{F}$

• $\frac{4}{9} \mathrm{F}$

• $\frac{\mathrm{F}}{4}$

A copper disc of radius 0.1 m is rotated about its centre with 20 rev/s in a uniform magnetic field of 0.1 T with its plane perpendicular to the field. The emf induced across the radius of the disc is

• $\frac{\mathrm{\pi }}{20} \mathrm{V}$

• $\frac{\mathrm{\pi }}{10} \mathrm{V}$

• $20 \mathrm{\pi } \mathrm{mV}$

• $10 \mathrm{\pi } \mathrm{mV}$

A magnetised wire of magnetic moment M and length L is bent in the form of a semi circle of radius r. The new magnetic moment is 

• M

• $\frac{\mathrm{M}}{2\mathrm{\pi }}$

• $\frac{\mathrm{M}}{\mathrm{\pi }}$

• $\frac{2\mathrm{M}}{\mathrm{\pi }}$

A proton, a deuteron and an alpha particle with the same kinetic energy enter a region of uniform magnetic field B at right angles to the field. The ratio of the radii of their circular paths is

• 1 : 1 : 1

• $1 : \sqrt{2} : \sqrt{2}$

• $\sqrt{2} : 1 : 1$

• $\sqrt{2} : \sqrt{2} : 1$

A solenoid 600 mm long has 50 turns on it and is wound on an iron rod of 7.5 mm radius. Find the flux through the solenoid when the current in it is 3 A. The relative permeability of iron is 600

• 1.66 Wb

• 1.66 n Wb

• 1.66 m Wb

• 1.66 μ Wb

An electric dipole is placed at an angle of 30° with an electric field ofintensity 2 × 10⁵ NC^-1. It experiences a torque equal to 4 Nm. Calculate the charge on the dipole if the dipole length is 2 cm.

• 8 mC

• 4 mC

• 2 mC

• 4 μC

Two identical cells send the same current in 3 Ω resistance, whether connected in series or in parallel. The internal resistance of the cell should be

• 1 Ω

• 3 Ω

• $\frac{1}{2} \mathrm{\Omega }$

• 3.5 Ω

Which ofthe following statement is incorrect ?

• In LCR series AC circuit, as the frequency of the source increases, the impedance of the circuit first decreases and then increases

• If the net reactance of an LCR series AC circuit is same as its resistance, then the current lags behind the voltage by 45°

• At resonance, the impedance of an AC circuit becomes purely resistive

• At resonance in LCR series AC circuit, the potential drops across inductor and capacitor are equal m magnitude but opposite in sign

49.

The plot represents the flow of current through a wire at three different times

                     

The ratio of charges flowing through the wire at different times is

• 2 : 1 : 2

• 1 : 3 : 3

• 1 : 1 : 1

• 2 : 3 : 4

A varying magnetic flux linking a coil is given by $\mathrm{\varphi } - {\mathrm{Xt}}^2$. If at time t = 3 s, the emf induced is 9 V, then the value of X is

• 0.66 Wb s^-2

• 1.5 Wb s^-2

• − 0.66 Wb s^-2

• − 1.5 Wb s^-2