Electromagnetic Induction

A conducting circular loop made of a thin wire, has area 3.5 $$\times$$ 10^$$-$$3 m² and resistance 10 $$\Omega$$. It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T)sin(50$$\pi$$t). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to :

A solid metal cube of edge length 2 cm is moving in a positive y-direction at a constant speed of 6 m/s. There is a uniform magnetic field of 0.1 T in the positive z-direction. The potential difference between the two faces of the cube perpendicular to the x-axis, is -

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate $${{dB} \over {dt}}$$ = 0.032 Ts^–1. The induced current in the loop is close to (Resistivity of the metal wire is 1.23 $$\times$$ 10^–8 $$\Omega$$m)

A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :

A long solenoid of radius R carries a time (t) - dependent current I(t)=I₀t(1 - t). A ring of radius 2R is placed coaxially near its middle. During the time interval 0 $$\le$$ t $$\le$$ 1, the induced current (I_R) and the induced EMF(V_R) in the ring change as :

Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by $$\phi$$_i. The magnetic flux through the area of the circular coil area is given by $$\phi$$₀. Which of the following option is correct?

An emf of $$0.08 \mathrm{~V}$$ is induced in a metal rod of length $$10 \mathrm{~cm}$$ held normal to a uniform magnetic field of $$0.4 \mathrm{~T}$$, when moves with a velocity of:

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be : (Assume the coil to be short circuited.)

The magnetic flux through a coil perpendicular to its plane is varying according to the relation $$\phi = (5{t^3} + 4{t^2} + 2t - 5)$$ Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at t = 2 s will be,

The electric current in a circular coil of 2 turns produces a magnetic induction B₁ at its centre. The coil is unwound and in rewound into a circular coil of 5 tuns and the same current produces a magnetic induction B₂ at its centre. The ratio of $${{{B_2}} \over {{B_1}}}$$ is