Identify the correctly matched pair

• Diamagnetic   —   Gadolinium

• Soft ferromagnetic   —   Alnico

• Hard ferromagnetic   —   Copper

• Paramagnetic   —   Sodium

If the radius of the dees of cyclotron is r, then the kinetic energy of a proton of mass m accelerated by the cyclotron at an oscillating frequency v is

• $4{\mathrm{\pi }}^2{\mathrm{m}}^2{\mathrm{v}}^2{\mathrm{r}}^2$

• $4{\mathrm{\pi }}^2{\mathrm{mv}}^2{\mathrm{r}}^2$

• $2{\mathrm{\pi }}^2{\mathrm{mv}}^2{\mathrm{r}}^2$

• ${\mathrm{\pi }}^2{\mathrm{mv}}^2{\mathrm{r}}^2$

If a magnetic dipole of moment M situated in the direction of a magnetic field B is rotated by 180°, then the amount of work done is

• MB

• 2 MB

• $\frac{\mathrm{MB}}{\sqrt{2}}$

• Zero

The polarity of induced emf is given by

• Ampere's circuital law

• Biot-Savart's law

• Lenz's law

• Fleming's right hand rule

In an L-C-R series circuit, at resonance

• the current and voltage are in phase

• the impedance is maximum

• the current is minimum

• the quality factor is independent of R

A conducting ring of radius 1 m kept in a uniform magnetic field B of 0.01 T, rotates uniformly with an angular velocity 100 rads^-1 with its axis of rotation perpendicular to B. The maximum induced emf in it is

• $1.5 \mathrm{\pi } \mathrm{V}$

• $\mathrm{\pi } \mathrm{V}$

• $2\mathrm{\pi } \mathrm{V}$

• $0.5 \mathrm{\pi } \mathrm{V}$

A step-down transformer increases the input current 4 A to 24 A at the secondary. If the number of turns in the primary coil is 330, the number of turns in the secondary coil is

• 60

• 50

• 55

• 45

In a plane electromagnetic wave, the electric field of amplitude 1 Vm^-1 varies with time in free space. The average energy density of magnetic field is (in Jm^-2)

• 8.86 × 10^-12

• 4.43 × 10^-12

• 17.72 × 10^-12

• 2.21 × 10^-12

Which one of the following is the property of a monochromatic, plane electromagnetic wave in free space?

• Electric and magnetic fields have a phase difference of $\frac{\mathrm{\pi }}{2}$

• The energy contribution of both electric and magnetic fields are equal.

• The direction of propagation is in the direction of electric field E

• The pressure exerted by the wave is the product of energy density and the speed of the wave

50.

A plane square sheet of charge of side 0.5 m has uniform surface charge density. An electron at 1 cm from the centre of the sheet experiences a force of 1.6 x 10^-12 N directed away from the sheet. The total charge on the plane square sheet is (ε₀ = 8.854 × 10^-12 C² m^-2 N^-1)

• 16.25 µC

• − 22.15 µC

• − 44.27 µC

• 144.27 µC