A proton, a deuteron and an alpha particle, after being accelerated through the same potential difference, enter a region of uniform magnetic field B → , in a direction perpendicular to B → . Compare their kinetic energies. If the radius of proton’s circular path is 5 cm , what will be the radii of the paths of deuteron and alpha particle?

The kinetic energy ( K ) of a charged particle for a given potential difference ( V ) is given as, K = q V Hence, for a given potential difference the kinetic energy of a charged particle is proportional to its charge. We know the ratio of charge between a proton, a deuteron and an alpha particle, q p : q d : q α = e : e : 2 e = 1 : 1 : 2 Hence the ratio of kinetic energy, K p : K d : K α = 1 : 1 : 2 Radius of the circular path of any particle of kinetic energy K r = m v q B = m q B . 2 K m = 2 m K q B For proton, r p = 2 m p k p e B = 5 cm For deuteron, r d = 2 m d k d e B = 2 × m p × k p e B = 2 r p = 1 .414 × 5 cm = 7 .07 cm For α -particle, r α = 2 m α k α e B = 2 × 4 × m p × 2 k p 2 e B = 2 r p = 10 cm

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What should be the minimum magnitude and direction of the magnetic field that must be produced at the equator of earth so that a proton may go around the earth with a speed of $1.0 \times 10^{7} {ms}^{- 1}$ ? Earth’s radius is $6.4 \times 10^{6} m .$

Important Questions on Magnetic Effect of Current

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12th CBSE

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New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Problems For Practice>Q 10

A stream of charged particles possessing a range of speeds enters region $I$ after passing through a slit $S_{1}$ (Fig. $4.67$ ). In $I$ region I there exist crossed (perpendicular) electric and magnetic fields. The electric field has magnitude $100 V m^{- 1}$ We want the particles emerging from slit $S_{2}$ into region $I I$ to have a fixed velocity of $1000 {ms}^{- 1}$ . What should be the value of the uniform magnetic field in region $I$ ?

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12th CBSE

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New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Problems For Practice>Q 11

A proton, a deuteron and an alpha particle, after being accelerated through the same potential difference, enter a region of uniform magnetic field

\vec{B}

, in a direction perpendicular to

\vec{B}

. Compare their kinetic energies. If the radius of proton’s circular path is

5 cm

, what will be the radii of the paths of deuteron and alpha particle?

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12th CBSE

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New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Problems For Practice>Q 12

A particle having a charge of

5.0 μ C

μC and a mass of

5.0 \times 10^{- 12} kg

is projected with a velocity of

1.0 km s^{- 1}

in a magnetic field of magnitude

5.0 m T

. The angle between the magnetic field and the velocity is

\sin^{- 1} (0.90)

. Show that the path of the particle will be a helix. Find the diameter of the helix and its pitch.

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12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Problems for Practice>Q 1

An electron of energy

10, 000 e V

describes a circular path in a plane at right angles to a uniform magnetic field of

0.01 T

. (a) What is the radius of the circular orbit? (b) What is the cyclotron frequency? (c) What is the period of its revolution? (d) What is the direction of revolution as viewed by an observer looking in the direction of the field?

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12th CBSE

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New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Problems for Practice>Q 2

The protons are accelerated by a cyclotron, when a magnetic field of

2.0 T

2.0 T is applied perpendicular to the plane of the dees. Calculate the energy of the proton in

M e V

MeV, if the circular path of the protons has a radius of

40 cm

before the protons leave the cyclotron. Given mass of a proton

= 1.67 \times 10^{- 27} kg

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12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Problems for Practice>Q 3

A cyclotron has an oscillatory frequency of

12 M H z

12 MHz and a dee radius of

50 cm

. Calculate the magnetic required to accelerate deuterons of mass

3.3 \times 10^{- 2} kg

and charge

1.6 \times 10^{- 19} C

. What is the energy of the deuterons emerging from the cyclotron?

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12th CBSE

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New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Problems for Practice>Q 4

Alpha particles of mass

6 .68 \times 10^{- 27} kg

and charge

3.2 \times 10^{- 19} C

are accelerated in a cyclotron in which a magnetic field of

1.25 T

is applied perpendicular to the dees. How rapidly should the electric field between the dees be reversed? What are the velocity and kinetic energy of an alpha particle when it moves in a circular orbit of radius

25 cm

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12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 4 - Magnetic Effect of Current>Problems for Practice>Q 1

A current of

1 A

flows in a wire of length

0.1 m

in a magnetic field of

0.5 T

. Calculate the force acting on the wire when the wire makes an angle of (a)

90 °

(b)

0 °

, with respect to the magnetic field.

What should be the minimum magnitude and direction of the magnetic field that must be produced at the equator of earth so that a proton may go around the earth with a speed of 1.0×107 ms-1? Earth’s radius is 6.4×106 m.

Important Questions on Magnetic Effect of Current

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What should be the minimum magnitude and direction of the magnetic field that must be produced at the equator of earth so that a proton may go around the earth with a speed of $1.0 \times 10^{7} {ms}^{- 1}$ ? Earth’s radius is $6.4 \times 10^{6} m .$