Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area A = 10 cm2 and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is (µ₀ = 4π × 10^-7 Tm A^-1) 

• 2.4 π × 10^-5 H

• 4.8 π × 10^-4 H

• 4.8 π × 10^-5 H

• 4.8 π × 10^-5 H

A horizontal overhead power line is at a height of 4m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is (µ₀ = 4π × 10^-7 T m A^-1)

• 2.5 × 10^-7 T southward

• 5 × 10^-6 T northward

• 5 × 10^-6 T southward

• 5 × 10^-6 T southward

Relative permittivity and permeability of a material are ε_r and µ_r, respectively. Which of the following values of these quantities are allowed for a diamagnetic material?

• εr = 0.5, µ_r = 1.5 

• ε_r = 1.5, µ_r = 0.5

• ε_r = 0.5, µ_r = 0.5

• ε_r = 0.5, µ_r = 0.5

The potential at a point x (measured in µm) due to some changes situated on the x-axis is given by V (x) = 20 /x²- 4) volts. The electric field E at x = 4 µm is given by

• 5/3 Volt/µm and in the –ve x direction

• 5/3 Volt/µm and in the +ve x direction

• 10/9 Volt/µm and in the -ve x direction

• 10/9 Volt/µm and in the -ve x direction

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a

• circle

• helix

• straight line

• straight line

In an AC generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency ω in a magnetic field B. The maximum value of emf generated in the coil is ‘

• N.A.B.ω

• N.A.B.R.ω

• N.A.B

• N.A.B

A long solenoid has 200 turns per cm and carries a current i. The magnetic field at its centre is 6.28 × 10⁻² Weber/m². Another long solenoid has 100 turns per cm and it carries a current i/3. The value of the magnetic field at its centre is

• 1.05 × 10⁻⁴ Weber/m²

• 1.05 × 10⁻² Weber/m²

• 1.05 × 10⁻³ Weber/m²

• 1.05 × 10⁻³ Weber/m²

A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 divisions per milliampere and voltage sensitivity is 2 divisions per millivolt. In order that each division reads 1 volt, the resistance in ohms needed to be connected in series with the coil will be

• 10³

• 10⁵

• 99995

• 99995

19.

In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will be

• 200Ω

• 100Ω

• 500 Ω

• 500 Ω

One conducting U tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. if each tube moves towards the other at a constant speed V, then the emf induced in the circuit in terms of B,

• B

• -B

• zero

• zero