Force Acting on Moving Charges

Practice Questions:

Question 1: moderate

An electric field E and a magnetic field B applied on a proton which moves with velocity v, it goes undeflected through the region if :

1. E ⊥ B

2. E is parallel to v and perpendicular to B

3. E, B and v all three mutually perpendicular to each other and v = E/B

4. E and B both are parallel but perpendicular to v

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Question 2: moderate

A particle having charge of 1 C, mass 1 kg and speed 1 m/s enters a uniform magnetic field, having magnetic induction of 1 T, at an angle θ = 30° between velocity vector and magnetic induction. The pitch of its helical path is (in meters)

1. \[\frac{\sqrt{3}\pi}{2}\]

2. \[\sqrt{3}\pi\]

3. π/2

4. π

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Question 3: moderate

An electron moves in the plane of the page through two regions of space along the
dotted-line trajectory shown in the figure. There is a uniform electric field in Region-I directed
into the plane of the page (as shown). There is no electric field in Region-II. What is a
necessary direction of the magnetic field in regions I and II ? Ignore gravitational forces.

1. Region-I Down the plane of the page Region-II Up the plane of the page

2. Region-I Up the plane of the page Region-II Into the plane of the page

3. Region-I Up the plane of the page Region-II Out of the plane of the page

4. Region-I Down the plane of the page Region-II Out of the plane of the page

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Question 4: moderate

A charge q coulomb moves in a circle with n revolutions per second and the radius of the circle is r metre. The magnetic field at the centre of the circle is :

1. \[\frac{2\pi q}{nr}\times10^{-7}NA^{-1}m^{-1}\]

2. \[\frac{2\pi q}{r}\times10^{-7}NA^{-1}m^{-1}\]

3. \[\frac{2\pi nq}{r}\times10^{-7}NA^{-1}m^{-1}\]

4. \[\frac{2\pi q}{r}\times NA^{-1}m^{-1}\]

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Question 5: moderate

A charged particle moves along a circle under the action of possible constant electric and magnetic fields. Which of the following are possible ?

1. E = 0, B = 0

2. E = 0, B ≠ 0

3. E ≠ 0, B = 0

4. E ≠ 0, B ≠ 0

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Question 6: moderate

Two particles Y and Z emitted by a radioactive source at P made tracks in a chamber as illustrated in the figure. A magnetic field acts downward into the paper. Careful measurements showed that both tracks were circular, the radius of Y track being half that of the Z track. Which one of the following statements is certainly true ?

1. Both particles Y and Z carried a positive charge

2. The mass of particle Z was one half that of particle Y

3. The mass of particle Z was twice that of particle Y

4. The charge of particle Z was twice that of particle Y

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Question 7: moderate

A charged particle enters a uniform magnetic field with velocity vector at an angle of 45° with the magnetic field. The pitch of the helical path followed by the particle is p. The radius of circle of the helix will be :

1. p/√2π

2. √2p

3. p/2π

4. √2p/π

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Question 8: moderate

A proton is moving along y-axis with velocity 200 m/s & magnetic field of magnitude 1 μT is acting at 30° angle to the y-axis. Then radius of circle in its helical path will be :

1. 2 m

2. 1 cm

3. 1 m

4. 0.1 m

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Question 9: moderate

An eΘ is moving in a zero gravity region towards upward direction & magnetic field in this region is along east direction. Then what will be the direction of electric field in this region so that eΘ can remain undeflected :

1. North

2. South

3. East

4. West

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Question 10: moderate

The acceleration of an eΘ at a certain moment in a magnetic field

\[\overrightarrow{B}=2\hat{i}+3\hat{j}+4\hat{k}\] is

\[\overrightarrow{a}=x\hat{i}+\hat{j}-\hat{k}\] .

The value of x is :

1. 0.5

2. 1

3. 2.5

4. 1.5

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