Moving Charges and Magnetism Difficult Questions and Answers | Page - 4

Moving Charges and Magnetism

A uniform magnetic field acts at right angles to the direction of motion of electron. As a result, the electron moves in a circular path of radius 2cm. If the speed of electron is doubled, then the radius of the circular path will be

1. 2.0 cm
1. 0.5 cm
1. 4.0 cm
1. 1.0 cm

View Hint View Answer Discuss in Forum

r = mv or r ∝ v
qB

As v is doubled, the radius also becomes double. Hence, radius = 2 × 2 = 4 cm

Correct Option: C

r = mv or r ∝ v
qB

As v is doubled, the radius also becomes double. Hence, radius = 2 × 2 = 4 cm

A deuteron of kinetic energy 50 keV is describing a circular orbit of radius 0.5 metre in a plane perpendicular to the magnetic field B. The kinetic energy of the proton that describes a circular orbit of radius 0.5 metre in the same plane with the same B is

1. 25 keV
1. 50 keV
1. 200 keV
1. 100 keV

View Hint View Answer Discuss in Forum

For a charged particle orbiting in a circular path in a magnetic field
mv² = Bqv ⇒ v = Bqr
r m

or, mv² = Bqvr
Also,
E_K = 1 mv² = 1 Bqvr = Bq. r . Bqr = B²q²r²
2 2 2 m 2m

For deuteron, E₁ = B²q²r²
2 × 2m

For proton, E₂ = B²q²r²
2m

= E₁ = 1 ⇒ 50 KeV = 1 ⇒ E₂ = 100 keV
E₂ 2 E₂ 2

Correct Option: D

For a charged particle orbiting in a circular path in a magnetic field
mv² = Bqv ⇒ v = Bqr
r m

or, mv² = Bqvr
Also,
E_K = 1 mv² = 1 Bqvr = Bq. r . Bqr = B²q²r²
2 2 2 m 2m

For deuteron, E₁ = B²q²r²
2 × 2m

For proton, E₂ = B²q²r²
2m

= E₁ = 1 ⇒ 50 KeV = 1 ⇒ E₂ = 100 keV
E₂ 2 E₂ 2

A charge moving with velocity v in X-direction is subjected to a field of magnetic induction in negative X-direction. As a result, the charge will

1. remain unaffected
1. start moving in a circular path Y–Z plane
1. retard along X-axis
1. move along a helical path around X-axis

View Hint View Answer Discuss in Forum

The force acting on a charged particle in magnetic field is given by
^→_F = q (^→_v × ^→_B) or F = qvB sin θ,
When angle between v and B is 180°, F = 0

Correct Option: A

The force acting on a charged particle in magnetic field is given by
^→_F = q (^→_v × ^→_B) or F = qvB sin θ,
When angle between v and B is 180°, F = 0

An electron enters a region where magnetic field (B) and electric field (E) are mutually perpendicular, then

1. it will always move in the direction of B
1. it will always move in the direction of E
1. it always possesses circular motion
1. it can go undeflected also

View Hint View Answer Discuss in Forum

When the deflection produced by electric field is equal to the deflection produced by magnetic field, then the electron can go undeflected.

Correct Option: D

When the deflection produced by electric field is equal to the deflection produced by magnetic field, then the electron can go undeflected.

A beam of electrons is moving with constant velocity in a region having simultaneous perpendicular electric and magnetic fields of strength 20 Vm^-1 and 0.5 T respectively at right angles to the direction of motion of the electrons. Then the velocity of electrons must be

1. 8 m/s
1. 20 m/s
1. 40 m/s
1. 1/40 m/s

View Hint View Answer Discuss in Forum

The electron moves with constant velocity without deflection. Hence, force due to magnetic field is equal and opposite to force due to electric field.
qvB = qE ⇒ v = E = 20 = 40 m/s
B 0.5

Correct Option: C

The electron moves with constant velocity without deflection. Hence, force due to magnetic field is equal and opposite to force due to electric field.
qvB = qE ⇒ v = E = 20 = 40 m/s
B 0.5