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?

• ε_r = 0.5, µ_r = 1.5

• ε_r = 1.5, µ_r = 0.5

• ε_r = 0.5, µr = 0.5

• ε_r = 0.5, µr = 0.5

Consider a block of conducting material of resistivity ‘ρ’ shown in the figure. Current ‘I’ enters at ‘A’ and leaves from ‘D’. We apply superposition principle to find voltage ‘∆V’ developed between ‘B’ and ‘C’. The calculation is done in the following steps:
(i) Take current ‘I’ entering from ‘A’ and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field E(r) at distance ‘r’ from A by using Ohm’s law E = ρj, where j is the current per unit area at ‘r’.
(iii) From the ‘r’ dependence of E(r), obtain the potential V(r) at r.
(iv) Repeat (i), (ii) and (iii) for current ‘I’ leaving ‘D’ and superpose results for ‘A’ and ‘D’.


For current entering at A, the electric field at a distance ‘r’ from A is

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 thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range 0 ≤ r< ∞ , where r is the distance from the centre of the shell? 

A 5V battery with internal resistance 2Ω and a 2V battery with internal resistance 1Ω are connected to a 10Ω resistor as shown in the figure. The current in the 10 Ω resistor is 

• 0.27 A P₂ to P₁

• 0.03 A P₁ to P₂

• 0.03 A P₂ to P₁

• 0.03 A P₂ to P₁

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

27.

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

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see in the figure).



If a strong diffraction peak is observed when electrons are incident at an angle ‘i’ from the normal to the crystal planes with distance’ between them (see figure), de Broglie wavelength λdB of electrons can be calculated by the relationship (n is an integer) 

• d sin i = nλ_dB

• 2d cos i = nλ_dB

• 2d sin i = nλ_dB

• 2d sin i = nλ_dB

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see in the figure).



In an experiment, electrons are made to pass through a narrow slit of width’ comparable to their de Broglie wavelength. They are detected on a screen at a distance ‘D’ from the slit (see figure). 

Which of the following graph can be expected to represent the number of electrons ‘N’ detected as a function of the detector position ‘y’(y = 0 corresponds to the middle of the slit)? 

This question contains Statement -1 and Statement-2. Of the four choices given after the statements,
Choose the one that best describes the two statements.
Statement – I: Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion.
and
Statement – II: For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it decreases with increasing Z.

• Statement – 1is false, Statement – 2 is true.

• Statement – 1is true, Statement – 2 is true; Statement -2 is correct explanation for Statement-1.

• Statement – 1is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.

• Statement – 1is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.