Advertisements
Advertisements
Question
A line charge λ per unit length is lodged uniformly onto the rim of a wheel of mass M and radius R. The wheel has light non-conducting spokes and is free to rotate without friction about its axis (Figure). A uniform magnetic field extends over a circular region within the rim. It is given by,
B = − B0 k (r ≤ a; a < R)
= 0 (otherwise)
What is the angular velocity of the wheel after the field is suddenly switched off?
Advertisements
Solution
Line charge per unit length = λ = `"Total charge"/"Length"` = `"Q"/(2π"r")`
Where,
r = Distance of the point within the wheel
Mass of the wheel = M
Radius of the wheel = R
Magnetic field, `vec"B" = -"B"_0hat"k"`
At distance r,themagnetic force is balanced by the centripetal force i.e.,
`"BQv" = ("mv"^2)/"r"`
Where
v = linear velocity of the wheel
∴ `"B"2pi"r"lambda = ("Mv")/"r"`
`"v" = ("B"2pilambda"r"^2)/"M"`
∴ Angular velocity, `omega = "v"/"r" = ("B"2pilambda"r"^2)/("MR")`
For r ≤ and a < R, we get:
`omega = -(2pi"B""aa"^2lambda)/("MR")hat"k"`
APPEARS IN
RELATED QUESTIONS
An emf of 2V is induced in a coil when the current in it is changed from 0A to 10A in 0·40 sec. Find the coefficient of self-inductance of the coil.
Explain why, the core of an electromagnet should be of soft iron and not of steel.
When current is 'switched on' and 'switched off' in a coil, a current is induced in another coil kept near it. What is this phenomenon known as?
An induced current is produced when a magnet is moved into a coil. The magnitude of induced current does not depend on:
(a) the speed with which the magnet is moved
(b) the number of turns of the coil
(c) the resistivity of the wire of the coil
(d) the strength of the magnet
Welders wear special goggles or face masks with glass windows to protect their eyes from electromagnetic radiations. Name the radiations and write the range of their frequency.
Consider the energy density in a solenoid at its centre and that near its ends. Which of the two is greater?
Can a transformer work when it is connected to a D.C. source? Give a reason.
Fill in the blanks by writing (i) Only soft iron, (ii) Only steel, (iii) Both soft-iron and steel for the material of core and/or magnet.
A. C. generator______.
State the purpose of soft iron core used in making an electromagnet.
You have been provided with a solenoid AB.
(i) What is the polarity at end A?
(ii) Give one advantage of an electromagnet over a permanent magnet.
Fleming's left hand rule : electric current : : Fleming's right hand rule : _______
State Lenz’s law.
Obtain an expression for motional emf from Lorentz force.
A closely wound circular coil of radius 0.02 m is placed perpendicular to the magnetic field. When the magnetic field is changed from 8000 T to 2000 T in 6 s, an emf of 44 V is induced in it. Calculate the number of turns in the coil.
Using Lenz’s law, predict the direction of induced current in conducting rings 1 and 2 when the current in the wire is steadily decreasing.
A cylindrical bar magnet is kept along the axis of a circular coil. If the magnet is rotated about its axis, then ____________.
A cylindrical bar magnet (A) and similar unmagnetized cylindrical iron bar (B) are dropped through metallic pipe. The time taken to come down by ____________.
Ansari Sir was demonstrating an experiment in his class with the setup as shown in the figure below.
A magnet is attached to a spring. The magnet can go in and out of the stationary coil. He lifted the Magnet and released it to make it oscillate through the coil.
Based on your understanding of the phenomenon, answer the following question.
What is the principle which Ansari Sir is trying to demonstrate?
A rectangular, a square, a circular and an elliptical loop, all in the (x - y) plane, are moving out of a uniform magnetic field with a constant velocity `vecv = vhati`. The magnetic field is directed along the negative z-axis direction. The induced emf, during the passage of these loops, out of the field region, will not remain constant for ______.
One solenoid is centered inside another. The outer one has a length of 50.0 cm and contains 6750 coils, while the coaxial inner solenoid is 3.0 cm long and π cm2 in area and contains 150 coils. The current in the outer solenoid is changing at 3000 A/s. The emf induced in the inner solenoid is ______ V.
(Round off to two decimal places.)
