Consider the motion of a charged particle of mass ‘ m ’ and charge ‘ q ’ moving with velocity v → in a magnetic field B → . If v → is perpendicular to B → , show that it describes a circular path having angular frequency ω = q B / m .

A magnetic force acts on the charged particle in a direction perpendicular to both v → and B → and provides centripetal force. Since v → is perpendicular to B → the angle between them is 90 ° . ∴ Magnetic force, F = q v B sin 90 ° = q v B This magnetic force will provide the centripetal force, F = q v B = m v 2 r ⇒ r = m v q B ∴ ω = v r = q B m

Consider the motion of a charged particle of mass ‘ m ’ and charge ‘ q ’ moving with velocity v → in a magnetic field B → . If the velocity v → has a component parallel to the magnetic field B → , trace the path described by the particle. Justify your answer.

If the velocity v → has a component parallel to the magnetic field B → . The parallel component of velocity will remains unaffected by the magnetic field and so the charged particle will continue to move along the field apart from moving in the circle due to the component of velocity perpendicular to the field and the resultant path will be a helix as shown in the figure.

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

Show that the kinetic energy of the particle moving in a magnetic field remains constant.

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 14

Consider the motion of a charged particle of mass

‘ m ’

and charge

‘ q ’

moving with velocity

\vec{v}

in a magnetic field

\vec{B}

. If

\vec{v}

is perpendicular to

\vec{B}

, show that it describes a circular path having angular frequency

ω = q B / m

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Text Based Exercises>Q 14

Consider the motion of a charged particle of mass

‘ m ’

and charge

‘ q ’

moving with velocity

\vec{v}

in a magnetic field

\vec{B}

. If the velocity

\vec{v}

has a component parallel to the magnetic field

\vec{B}

, trace the path described by the particle. 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 15

A uniform magnetic field

\vec{B}

is set up along the positive

X

-axis. A particle of charge

' q'

and mass

' m'

moving with a velocity

\vec{v}

enters the field at the origin in

X - Y

plane such that it has velocity components both along and perpendicular to the magnetic field

\vec{B}

. Trace, giving reason, the trajectory followed by the particle. Find out the expression for the distance moved by the particle along the magnetic field in one rotation.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Text Based Exercises>Q 16

Find the condition under which the charged particles moving with different speeds in the presence of electric and magnetic field vectors can be used to select charged particles of a particular speed.

EASY

12th CBSE

IMPORTANT

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

Obtain the expression for the cyclotron frequency.

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?

Show that the kinetic energy of the particle moving in a magnetic field remains constant.

Important Questions on Magnetic Effect of Current

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