Two concentric coils each of radius equal to 2 $\mathrm{\pi }$ cm are placed at right angles to each other. If 3A and 4A are the currents flowing through the two coils respectively. The magnetic induction (in Wb m^-2) at the centre of the coils will be

• 5 × 10^-5

• 12 × 10^-5

• 7 × 10^-5

• 10^-5

Two coils have a mutual inductance 0.005 H. The current changes in the first coil according to the equation I = i_m sin ωt, where i_m = 10 A and ω = 100 rad s^-1. The maximum value of the emf induced in the second coil is

• $\mathrm{\pi }$

• $2\mathrm{\pi }$

• $4\mathrm{\pi }$

• $5\mathrm{\pi }$

A wheel with 10 spokes each of length L m is rotated with a uniform angular velocity ω in a plane normal to the magnetic field B. The emf induced between the axle and the rim of the wheel is

• $\frac{1}{2} {\mathrm{N\omega BL}}^2$

• $\frac{1}{2} {\mathrm{\omega BL}}^2$

• ${\mathrm{\omega BL}}^2$

• NωBL²

When 100 V DC is applied across a coil, a current of 1 A flows through it. When 100 V AC of50 Hz is applied to the same coil only 0.5 A flows. The inductance of the coil is

• 5.5 mH

• 0.55 mH

• 55 mH

• 0.55 H

An aluminium ring B faces an electromagnet A. The current I through A can be altered. Then which of the following statements is correct ?

• If I decreases, A will repel B

• Whether I increases or decreases, B will not experience any force

• If I increases, A will repel B

• If I increases, A will attract B

A long solenoid has 1000 turns. when a current of 4 A flows through it, the magnetic flux linked with each turn of the solenoid is 4x10^-3 Wb. The self inductance of the solenoid is,

• 3H

• 2H

• 1H

• 1H

An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude.

• 

• zero

• 
• 

A conducting square frame of side 'a' and a long straight wire carrying current I are located in the same plane as shown n the figure. The frame moves to the right with constant velocity 'v'. The emf induced in the frame will be proportional to

49.

A coil of resistance 400 is placed in magnetic field. If the magnetic flux Φ (Wb) linked with the coil varies with time t  (sec) as Φ = 50t² +4.
The current in the coil at t= 2 s is

• 0.5 A

• 0.1 A

• 2 A

• 2 A

A thin semicircular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B, as shown in figure. The potential difference developed across the ring when its speed is v, is

• zero

•  is at higher potential
•  and R is at higher potential
•  and R is at higher potential