Capacitance of a parallel plate capacitor becomes $\frac{3}{2}$ times its original value if a dielectric slab of thickness $\frac{\mathrm{d}}{2}$ is inserted between the plates, where d is the separation between the plates. The dielectric constant of the slab is

• 4

• 2

• 3

• 1

The electric potential V at any point x, y, z in space is given by V = 4 x² . The electric field at the point (2, 0, 1) in Vm^-1 is

• 10 $\stackrel{\wedge }{\mathrm{j}}$

• 20 $\stackrel{\wedge }{\mathrm{j}}$

• − 16 $\stackrel{\wedge }{\mathrm{i}}$

• 30 $\stackrel{\wedge }{\mathrm{i}}$

The electric field in a region is given by E = $\left(4 \stackrel{\wedge }{\mathrm{i}} + 3 \stackrel{\wedge }{\mathrm{j}}\right)$V/m. The net flux passing through a square area of side 4 m parallel to y-z plane is

• 32 V-m

• 16 V-m

• 12 V-m

• 64 V-m

The current in a wire varies with time as I = 5t² + 2t, where I is in ampere and t is in second. The quantity of charge which has to be passed through a cross-section of wire during the times t = 4 s to t = 6 s is

• 220 C

• 340 C

• 273.34 C

• 280 C

Three resistances of 2 Ω, 3 Ω and 6 Ω are connected in parallel and the combination is connected in series with 2 V battery having internal resistance of 1 Ω . The current in the battery is

• 1 A

• 3 A

• 2 A

• 4 A

An electric cable of copper has just one wire of radius 9 mm with resistance 5 Ω . This single copper wire of cable is replaced by 4 different well insulated copper wires each of radius 3 mm. The total resistance of the cable now will be

• 22.5 Ω

• 45 Ω

• 9 Ω

• 11.25 Ω

A rise of temperature 5°C is observed in a conductor by passing a current. If the current is doubled the rise in temperature will be

• 10°C

• 20°C

• 5°C

• 25°C

38.

The current density varies with radial distance r as J =ar² (where, a is a constant) in a  cylindrical wire of radius R. The current passing through the wire between radial distance $\frac{\mathrm{R}}{4}$ and $\frac{\mathrm{R}}{2}$ is 

• $\frac{20{\mathrm{\pi aR}}^4}{331}$

• $\frac{15{\mathrm{\pi aR}}^4}{512}$

• $\frac{{\mathrm{\pi aR}}^4}{332}$

• $\frac{3{\mathrm{\pi aR}}^4}{864}$

An electron having mass 9.1 x 10^-31 kg moves in a circular path of radius 0.4 m with velocity 10⁵ m/s in a magnetic field. The strength of magnetic field is

• 1.56 × 10^-5 T

• 1.62 × 10^-4 T

• 1.42 x 10^-6 T

• 1.88 × 10^-5 T

A current of 0.4 A is passed through the coil of galvanometer having 500 turns and each turn has an average area of 3 x 10^-4 m² . If a torque of 2 Nm is required for this coil carrying some current to set it parallel to a magnetic field then the strength of magnetic field will be

• 31 T

• 33.34 T

• 32 T

• 40 T