Charges & Magnetism Test

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Charges & Magnetism Test - 14

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Weekly Quiz Competition

Question 1
1 / -0

A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields  with a velocity  perpendicular to both , and comes out without any change in its magnitude or direction. Then

A

B

C

D

Solution

When  are perpendicular and velocity has no change then qE = qvB i.e. v= E/B. The two forces oppose each other so, v is along  i.e., .
As  are perpendicular to each other
Question 2
1 / -0

A charged particle would continue to move with a constant velocity in a region wherein, which of the following conditions is not correct?

A
E = 0,B ≠ 0

B
E ≠ 0 ,B ≠ 0

C
E ≠ 0 , B = 0

D
E = 0 , B = 0
Question 3
1 / -0

The cyclotron frequency v_c is given by

A
qB/2πm

B
mB/2πq

C
2πm/qB

D
2πm/qm

Solution

In cyclotron the centripetal force is balanced by magnetic force, then
qvB = mn²/r ⇒ qBr/m = v
where v = 2πrv_c∴ v_c = qB/2πm
Question 4
1 / -0

A charged particle is moving in a cyclotron, what effect on the radius of path of this charged particle will occur when the frequency of the radio frequency field is doubled?

A
It will also be doubled.

B
It will be halved.

C
It will be increased by four times.

D
It will remain unchanged.

Solution

As frequency of revolution in a cyclotron
v_C = Bq/2πm is independent of r.
So the radius of path in the dees will remain unchanged. When the frequency is changed.
Question 5
1 / -0

A cubical region of space is filled with some uniform electric and magnetic field. An electron enters the cube across one of its faces with velocity v and a positron enters via opposite face with velocity - v. At this instant, which one of the following is not correct?

A
The electric forces on both the particles cause identical accelerations.

B
The magnetic forces on both the particles cause equal acceleration.

C
Both particles gain or loose energy at the same rate.

D
The motion of the centre of mass is determined by B alone.
Question 6
1 / -0

A cyclotron is operated at an oscillator frequency of 12 MHz and has a dee radius R = 50 cm. What is the magnitude of the magnetic field needed for a proton to be accelerated in the cyclotron?

A
0.72 T

B
0.65 T

C
0.39 T

D
0.12 T
Question 7
1 / -0

If an electron is moving in a magnetic field of 5.4 x 10^-4 T on a circular path of radius 32 cm having a frequency of 2.5 MHz, then its speed will be

A
8.56 x 10⁶ m s^-1

B
5.024 x 10⁶ m s^-1

C
8.56 x 10⁴ m s^-1

D
5.024 x 10⁴ m s^-1

Solution

Here, B = 5.4 x 10^-4 T;
r = 32 cm = 32 x 10^-2 m; v = 2.5 MHz = 2.5 x 10⁶Hz
The speed of electron on circular path
v = r x 2πv = 32 x 10^-2 x 2 x 3.14 x 2.5 x 10⁶
= 502.4 x 10⁴ = 5.024 x 10⁶ m s^-1
Question 8
1 / -0

A proton and an α-partide enter in a unifoi magnetic field perpendicularly with same speed. The ratio of time periods of both particle (T_P/T_α) will be

A
1 : 2

B
1 : 3

C
2 : 1

D
3 : 1

Solution

The time period of revolution of a charged particle in a magnetic field is
T = 2πm/Bq
For proton, m_P = m, q_P = q ; ∴ T_P = 2πm/Bq
Now, for α-particle, m_α = 4m, q_α = 2q
∴ T_α = (2π(4m))/(B(Bq)) = 2(2πm/Bq) ⇒ T_P/T_α = 1/2
Question 9
1 / -0

A proton, a deutron and an α-particle with same, kinetic energy enter perpendicularly in a uniform magnetic field, then the ratio of radii of their circular paths is

A
1 : 1 : √2

B
√2 : 1 : 1

C
1 : √2 : 1

D
1 : 2 : √2

Solution

∵ r = ∴ r ∝ √m/q
Hence, r_p : r_d ; r_α =
=
Question 10
1 / -0

If an electron enters with a velocity into a cubical region in a uniform electromagnetic field and the orbit of the electron is found to spiral down inside the cube in plane parallel to x-y plane then the configuration of electric field and magnetic field is

A

B

C

D

Solution

The orbit of the electron spirals down inside the cube in the plane parallel to x−y plane. Therefore must be along +z direction and should be along x−axis.
Question 11
1 / -0

Which of the following is not correct about cyclotron?

A
It is a machine to accelerate charged particles or ions to high energies.

B
Cyclotron uses both electric and magnetic fields in combination to increase the energy of charged particles.

C
The operation of the cyclotron is based on the fact that the time for one revolution of an ion is independent of its speed or radius of its orbit.

D
The charged particles and ions in cyclotron can move on any arbitrary path.

Solution

The charged particles and ions in cyclotron can move along circular path only.
Question 12
1 / -0

The operating magnetic field for accelerating protons in a cyclotron oscillator having frequency of 12 MHz is (q = 1.6 x 10^-19C, m_p = 1.67 x 10^-27kg and 1 MeV = 1.6 x 10^-13 j)

A
0.69 T

B
0.79 T

C
0.59 T

D
0.49 T

Solution
Question 13
1 / -0

In the question number 34, the kinetic energy (in MeV) of the proton beam produced by the accelerator is (radius of dees = 60 cm)

A
5

B
6.5

C
10.6

D
12.6

Solution

Final velocity of proton is
v = r x 2πv = 0.6 x 2 x 3.14 x 12 x 10⁶ = 4.5 x 10⁷ m s^-1

= 10.6 MeV
Question 14
1 / -0

An electron is moving in a cyclotron at a speed of 3.2 x 10⁷ m s^-1 in a magnetic field of 5 x 10^-4 T perpendicular to it. What is the frequency of this electron?
(q = 1.6 x 10^-19 C, m_e = 9.1 x 10^-31 kg)

A
1.4 x 10⁵ Hz

B
1.4 x 10⁷ Hz

C
1.4 x 10⁶ Hz

D
1.4 x 10⁹ Hz

Solution

v = 3.2 x 10⁷ m s^-1 ;B = 5 x 10^-4 T
The frequency of electron is