Advertisements
Advertisements
Question
A conducting disc of radius r rotates with a small but constant angular velocity ω about its axis. A uniform magnetic field B exists parallel to the axis of rotation. Find the motional emf between the centre and the periphery of the disc.
Advertisements
Solution
The angular velocity of the disc is ω. Also, the magnetic field of magnitude B is perpendicular to the disc.
Let us take a circular element of thickness da at a distance a from the centre.
Linear speed of the element at a from the centre, v = ωa
Now,
\[de = Blv\]
\[de = B \times da \times a\omega\]
\[ \Rightarrow e = \int_0^r \left( B\omega a \right)da\]
\[ e = \frac{1}{2}B\omega r^2\]
APPEARS IN
RELATED QUESTIONS
Figure shows a straight, long wire carrying a current i and a rod of length l coplanar with the wire and perpendicular to it. The rod moves with a constant velocity v in a direction parallel to the wire. The distance of the wire from the centre of the rod is x. Find the motional emf induced in the rod.
An aircraft of wing span of 50 m flies horizontally in the Earth's magnetic field of 6 x 10-5 T at a speed of 400 m/s. Calculate the emf generated between the tips of the wings of the aircraft.
A metal disc of radius 30 cm spins at 20 revolution per second about its transverse symmetry axis in a uniform magnetic field of 0.20 T. The field is parallel to the axis of rotation. Calculate
(a) the area swept out per second by the radius of the disc
(b) the flux cut per second by a radius of the disc
(c) the induced emf between the axle and rim of the disc.
A cycle wheel of radius 0.6 m is rotated with constant angular velocity of 15 rad/s in a region of magnetic field of 0.2 T which is perpendicular to the plane of the wheel. The e.m.f generated between its center and the rim is, ____________.
The emf induced across the ends of a conductor due to its motion in a magnetic field is called motional emf. It is produced due to magnetic Lorentz force acting on the free electrons of the conductor. For a circuit shown in the figure, if a conductor of length l moves with velocity v in a magnetic field B perpendicular to both its length and the direction of the magnetic field, then all the induced parameters are possible in the circuit.
Direction of current induced in a wire moving in a magnetic field is found using ______.
The emf induced across the ends of a conductor due to its motion in a magnetic field is called motional emf. It is produced due to magnetic Lorentz force acting on the free electrons of the conductor. For a circuit shown in the figure, if a conductor of length l moves with velocity v in a magnetic field B perpendicular to both its length and the direction of the magnetic field, then all the induced parameters are possible in the circuit.
A 0.1 m long conductor carrying a current of 50 A is held perpendicular to a magnetic field of 1.25 mT. The mechanical power required to move the conductor with a speed of 1 ms-1 is ______.
The emf induced across the ends of a conductor due to its motion in a magnetic field is called motional emf. It is produced due to magnetic Lorentz force acting on the free electrons of the conductor. For a circuit shown in the figure, if a conductor of length l moves with velocity v in a magnetic field B perpendicular to both its length and the direction of the magnetic field, then all the induced parameters are possible in the circuit.
A bicycle generator creates 1.5 V at 15 km/hr. The EMF generated at 10 km/hr is ______.
Motional e.m.f is the induced e.m.f. ______
An e.m.f is produced in a coil, which is not connected to an external voltage source. This can be due to ______.
- the coil being in a time varying magnetic field.
- the coil moving in a time varying magnetic field.
- the coil moving in a constant magnetic field.
- the coil is stationary in external spatially varying magnetic field, which does not change with time.
A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. This can be because ______.
- the magnetic field is constant.
- the magnetic field is in the same plane as the circular coil and it may or may not vary.
- the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably.
- there is a constant magnetic field in the perpendicular (to the plane of the coil) direction.
A magnetic field B = Bo sin ( ωt )`hatk` wire AB slides smoothly over two parallel conductors separated by a distance d (Figure). The wires are in the x-y plane. The wire AB (of length d) has resistance R and the parallel wires have negligible resistance. If AB is moving with velocity v, what is the current in the circuit. What is the force needed to keep the wire moving at constant velocity?
A rod of mass m and resistance R slides smoothly over two parallel perfectly conducting wires kept sloping at an angle θ with respect to the horizontal (Figure). The circuit is closed through a perfect conductor at the top. There is a constant magnetic field B along the vertical direction. If the rod is initially at rest, find the velocity of the rod as a function of time.
Find the current in the sliding rod AB (resistance = R) for the arrangement shown in figure. B is constant and is out of the paper. Parallel wires have no resistance. v is constant. Switch S is closed at time t = 0.
Derive an expression for the total emf induced in a conducting rotating rod.
A magnetic flux associated with a coil changes by 0.04 Wb in 0.2 second. The induced emf with coil is ______.
A wire of length 1 m moving with velocity 8 m/s at right angles to a magnetic field of 2 T. The magnitude of induced emf, between the ends of wire will be ______.
Figure shows a rectangular frame situated in a constant magnetic field. A wire BC of length 1 m is moved out with velocity 4 m/s. Magnetic field strength is 0.15 T. Force acting on the wire BC is:
