Show that the frequency of revolution, of a charged particle (in the X - Y X-Y plane), in a uniform magnetic field B → B → = B k ^ ), is independent of its speed. Which practical machine makes use of this fact? What is the frequency of the alternating electric field, used in this machine?

The magnetic field B → = B k ^ is perpendicular to the X - Y plane. We know, when the magnetic field is perpendicular to the velocity then the particle moves in a circle. The required centripetal force is provided by the magnetic force. m v 2 r = q v B ⇒ r = m v q B Time taken by ion to describe a circular path is given by = 2 πr v ⇒ 2 πm q B The frequency f = 1 T = q B 2 πm Hence the frequency of the alternating electric field should also be equal to f = q B 2 πm A cyclotron makes use of this fact in which alternating electric field of frequency f is applied.

EASY

12th CBSE

IMPORTANT

Earn 100

Obtain the expression for the cyclotron frequency.

Important Questions on Magnetic Effect of Current

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Text Based Exercises>Q 17

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.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Text Based Exercises>Q 18

A hydrogen ion of mass

‘ m ’

and charge

‘ q ’

travels with a speed

‘ v ’

along a circle of radius

‘ r ’

in a uniform magnetic field of flux density

‘ B ’

. Obtain the expression for the magnetic force on the ion and determine its time period.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Text Based Exercises>Q 19

Show that the frequency of revolution, of a charged particle (in the

X - Y

X-Y plane), in a uniform magnetic field

\vec{B} (\vec{B} = B \hat{k})

), is independent of its speed. Which practical machine makes use of this fact? What is the frequency of the alternating electric field, used in this machine?

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Text Based Exercises>Q 20

Draw a schematic sketch of a cyclotron. Explain clearly the role of crossed electric and magnetic fields in accelerating the charge. Hence derive the expression for the kinetic energy acquired by the particles.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Text Based Exercises>Q 21

State the principle of a cyclotron. 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 ?

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Text Based Exercises>Q 22

Derive an expression for the maximum force experienced by a straight conductor of length

l

, carrying current

I

and kept in a uniform magnetic field,

B

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Text Based Exercises>Q 23

Two long straight parallel conductors carry steady currents

I_{1}

and

I_{2}

separated by a distance

d

. If the currents are flowing in the same direction, show how the magnetic field set-up in one produces an attractive force on the other. Obtain the expression for this force. Hence define one ampere.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Text Based Exercises>Q 24

Derive a formula for the force between two parallel straight conductors carrying current in opposite directions and write the nature of the force. Hence, define an ampere.

Obtain the expression for the cyclotron frequency.

Important Questions on Magnetic Effect of Current

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