Advertisements
Advertisements
प्रश्न
Figure shows a rod PQ of length 20.0 cm and mass 200 g suspended through a fixed point O by two threads of lengths 20.0 cm each. A magnetic field of strength 0.500 T exists in the vicinity of the wire PQ, as shown in the figure. The wires connecting PQ with the battery are loose and exert no force on PQ. (a) Find the tension in the threads when the switch S is open. (b) A current of 2.0 A is established when the switch S is closed. Find the tension in the threads now.
उत्तर
Given:
Length of the rod PQ = 20.0 cm
Mass of the rod, M = 200 g
Length of the two threads, l = 20.0 cm
Applied magnetic field, B = 0.500 T
As per the question,
(a) When the circuit is open:
The weight of the rod is balanced by the tension in the rod. So,
2Tcos30° = Mg
`T = (mg)/(2cos30^circ)`
=`(0.2xx9.8)/(2 (sqrt(3)/2)`
=1.13 N
(b) When the circuit is closed and current flowing through the circuit = 2 A:
Then,
2Tcos 30°= Mg + ilB
= 0.200× 9.8 + 2 × 0.2 × 0.5
= 1.95 + 0.2 = 2.16
⇒ `2T = 2.16xx (2)/(sqrt(3)`
⇒ T = 1.245 = 1.25 N
APPEARS IN
संबंधित प्रश्न
Show that the time period of revolution of particles in a cyclotron is independent of their speeds. Why is this property necessary for the operation of a cyclotron?
If a watch-glass containing a small quantity of water is placed on two dissimilar magnetic poles, then water ______.
Obtain the expression for the cyclotron frequency.
A deuteron and a proton are accelerated by the cyclotron. Can both be accelerated with the same oscillator frequency? Give reason to justify your answer.
Draw a schematic sketch of a cyclotron. Explain clearly the role of crossed electric and magnetic field in accelerating the charge. Hence derive the expression for the kinetic energy acquired by the particles.
An α-particle and a proton are released from the centre of the cyclotron and made to accelerate.
(i) Can both be accelerated at the same cyclotron frequency?
Give reason to justify your answer.
(ii) When they are accelerated in turn, which of the two will have higher velocity at the exit slit of the does?
A cyclotron is used to accelerate protons to a kinetic energy of 5 MeV. If the strength of magnetic field in the cyclotron is 2T, find the radius and the frequency needed for the applied alternating voltage of the cyclotron. (Given : Velocity of proton= `3xx10^7 m//s`)
An electron is projected horizontally with a kinetic energy of 10 keV. A magnetic field of strength 1.0 × 10−7 T exists in the vertically upward direction.
(a) Will the electron deflect towards the right or left of its motion?
(b) Calculate the sideways deflection of the electron while travelling through 1 m. Make appropriate approximations.
A conducting wire of length l, lying normal to a magnetic field B, moves with a velocity v,as shown in the figure. (a) Find the average magnetic force on a free electron of the wire. (b) Due to this magnetic force, electrons concentrate at one end, resulting in an electric field inside the wire. The redistribution stops when the electric force on the free electrons balances the magnetic force. Find the electric field developed inside the wire when the redistribution stops. (c) What potential difference is developed between the ends of the wire?
(a) An electron moves along a circle of radius 1 m in a perpendicular magnetic field of strength 0.50 T. What would be its speed? Is it reasonable? (b) If a proton moves along a circle of the same radius in the same magnetic field, what would be its speed?
Answer the following question.
State the underlying principle of a cyclotron. Explain its working with the help of a schematic diagram. Obtain the expression for cyclotron frequency.
A cyclotron's oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons? If the radius of its 'dees' is 60 cm, calculate the kinetic energy (in MeV) of the proton beam produced by the accelerator.
An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Its centripetal acceleration is ______.
A particle of mass m is moving in a circular path of constant radius r such that, its centripetal acceleration ac is varying with time t as ac = k2rt2, where k is a constant. The power delivered to the particle by the forces acting on it is ______.
The cyclotron was designed by ______
Verify that the cyclotron frequency ω = eB/m has the correct dimensions of [T]–1.
Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency (rf) field were doubled.
