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PHYSICS, M6 2024 HSC 15 MC

A uniform magnetic field is directed into the page. A conductor rotates about the end at a constant rate.
 

 
 

Which graph shows the emf induced between the ends of the conductor, and , as it rotates one revolution from the position shown?
 


 

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Show Worked Solution

→ As the conductor rotates in the magnetic field, all of the charges in the conductor will have a velocity.

→ This will produce a force on each positive and negative charge in the rod according to the equation .

→ Using the right hand rule, the direction of the force applied to each positive charge in the rod during the rotation will be towards . Similarly, the direction of force on each negative charge will be towards . 

→ This separation of positive and negative charges to opposite ends of the conductor generates the emf.

→ As the velocity of the charges during the circular motion will remain constant, the force on the charges will be constant. Therefore, a constant emf will be produced in the conductor.

♦♦ Mean mark 35%.

PHYSICS, M6 2019 VCE 1

A particle of mass and charge travelling at velocity enters a uniform magnetic field , as shown in Figure 1.
 

  1. Is the charge positive or negative? Give a reason for your answer.   (1 mark)
  1. Explain why the path of the particle is an arc of a circle while the particle is in the magnetic field.   (2 marks)

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a.    Using the right-hand rule:

→ Thumb is in direction of velocity (right) and fingers are in direction of B-field (Into the page).

→ As the force on the charge is down the page (back of the hand), the charge must be negative.
 

b.    For circular motion to occur:

→ The force must be at right-angles to the velocity of the particle.

→ The force must be of constant magnitude .

→ In the given example, the force on the charged particle due to the magnetic field is perpendicular to its velocity and the magnitude of the force remains constant.

→ The particle will therefore follow the arc of a circle while in the magnetic field.

Show Worked Solution

a.    Using the right-hand rule:

→ Thumb is in direction of velocity (right) and fingers are in direction of B-field (Into the page).

→ As the force on the charge is down the page (back of the hand), the charge must be negative.

♦ Mean mark (a) 44%.

b.    For circular motion to occur:

→ The force must be at right-angles to the velocity of the particle.

→ The force must be of constant magnitude .

→ In the given example, the force on the charged particle due to the magnetic field is perpendicular to its velocity and the magnitude of the force remains constant.

→ The particle will therefore follow the arc of a circle while in the magnetic field.

♦♦♦ Mean mark (b) 27%.

PHYSICS, M6 2020 VCE 3-4 MC

A positron with a velocity of 1.4 × 10 m s is injected into a uniform magnetic field of 4.0 × 10 T, directed into the page, as shown in the diagram below.

It moves in a vacuum in a semicircle of radius . The mass of the positron is 9.1 × 10 kg and the charge on the positron is 1.6 × 10 C. Ignore relativistic effects.
 


 

Question 3

Which one of the following best gives the speed of the positron as it exits the magnetic field?

  1. 0 m s
  2. much less than 1.4 × 10 m s
  3. 1.4 × 10 m s
  4. greater than 1.4 × 10 m s

 
Question 4

The speed of the positron is changed to 7.0 × 10 m s.

Which one of the following best gives the value of the radius for this speed?

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Show Worked Solution

→ As the direction of the force is perpendicular to the velocity, the velocity will not change.

→ The velocity will be


 

 
 
 

 
→ Therefore, .

→ If the velocity is halved, the radius will also be halved.

PHYSICS, M6 2023 VCE 1 MC

One type of loudspeaker consists of a current-carrying coil within a radial magnetic field, as shown in the diagram below. and are magnetic poles, and the direction of the current, , in the coil is clockwise as shown.
 


 

The force, , acting on the current-carrying coil is directed into the page.

Which one of the following statements correctly identifies the magnetic polarities of and ?

  1. is a north pole and is a south pole.
  2. is a south pole and is a north pole.
  3. Both and are north poles.
  4. Both and are south poles.
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Show Worked Solution

→ Using the right hand rule, the palm faces into the page (direction of the force) and thumb points down the page (direction of the current).

→ The direction of the magnetic field is from and (direction of fingers).

→ is a north pole and is a south pole.

PHYSICS, M6 2023 HSC 24

An electron is travelling at 3.0 10 m s in the path shown.
 

Calculate the magnetic field required to keep the electron in the path.  (3 marks)

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Show Worked Solution

→ The force from the magnetic field on the electron provides the centripetal acceleration for it to travel in uniform circular motion.

 
 
 
   
   

 
→ Magnetic field strength required = .

Mean mark 57%.

PHYSICS, M6 2015 HSC 8 MC

In which of the following situations does the magnetic field exert the greatest force on the proton ( ), given that all of the fields are of equal magnitude?

 

 

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→ The force on each proton is given by 

→ As and are the same in all four situations, the maximum force will occur when    is greatest.

A: 

B: 

C: 

D: 

PHYSICS, M6 2017 HSC 18 MC

A particle of mass and charge travelling at velocity enters a magnetic field of magnitude and follows the path shown.
 

A second particle enters a magnetic field of magnitude with a velocity of    and follows an identical path.

What is the mass and charge of the second particle?

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Show Worked Solution

The centripetal force acting on the charge is given by the force it experiences due to the magnetic field:

 
 
 

 

 
 

 


♦♦ Mean mark 35%.

PHYSICS, M6 2018 HSC 13 MC

An electron moves in a circular path with radius in a magnetic field as shown.
 

If the speed of the electron is increased, which row of the table correctly shows the effects of this change?

 

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Show Worked Solution

→ Using the formula  , increasing the speed of the electron increases the force acting on it.

→ The centripetal force acting on the electron is given by the force it experiences due to the magnetic field:

→ Increasing the speed of the electron increases its radius.


Mean mark 53%.

PHYSICS, M6 2019 HSC 33

A proton and an alpha particle are fired into a uniform magnetic field with the same speed from opposite sides as shown. Their trajectories are initially perpendicular to the field.
 


  

Explain ONE similarity and ONE difference in their trajectories as they move in the magnetic field.   (4 marks)

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Similarity:

→ Both particles experience a constant force, given by  , perpendicular to their velocity and the magnetic field lines and will undergo circular motion.

Difference:

→ The centripetal force acting on both particles is given by the force they experience due to the magnetic field as follows:

→ The alpha particle has four times the mass and two times the charge of the proton

→ Therefore, the radius of its trajectory will be twice that of the protons.

Show Worked Solution

Similarity:

→ Both particles experience a constant force, given by  , perpendicular to their velocity and the magnetic field lines and will undergo circular motion.

Difference:

→ The centripetal force acting on both particles is given by the force they experience due to the magnetic field as follows:

→ The alpha particle has four times the mass and two times the charge of the proton

→ Therefore, the radius of its trajectory will be twice that of the protons.

PHYSICS M6 2022 HSC 34

Three charged particles, and , travelling along straight, parallel trajectories at the same speed, enter a region in which there is a uniform magnetic field which causes them to follow the paths shown. Assume that the particles do not exert any significant force on each other.
 


 

Explain the different paths that the particles follow through the magnetic field.   (7 marks)

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→ The charged particles each experience a force equal to    as they travel perpendicular to the magnetic field lines.

→ This force acts perpendicular to the direction of their velocity, so the charged particles undergo uniform circular motion with the force due to the magnetic field acting as a centripetal force.

→ The radii of their paths can be described by the equation:

 
 
 

 
→ As the strength of the magnetic field and the speed of the particles is the same, their trajectory is only affected by their mass to charge ratio   which affects their radius of motion and their sign, which determines the direction which they deflect.

→ Both and initially curve upwards, using the right hand palm rule, these must both be positive charges.

→  has a greater radius than , so ’s charge to mass ratio is greater than ’s.

→ initially curves downwards, using the right hand palm rule, it must have a negative charge.

→ has the same radius of motion as , so the charge to mass ratios of and are the same.

→ has a smaller radius than , so ’s charge to mass ratio is less than that of .

Show Worked Solution

→ The charged particles each experience a force equal to    as they travel perpendicular to the magnetic field lines.

→ This force acts perpendicular to the direction of their velocity, so the charged particles undergo uniform circular motion with the force due to the magnetic field acting as a centripetal force.

→ The radii of their paths can be described by the equation:

 
 
 

 
→ As the strength of the magnetic field and the speed of the particles is the same, their trajectory is only affected by their mass to charge ratio   which affects their radius of motion and their sign, which determines the direction which they deflect.

→ Both and initially curve upwards, using the right hand palm rule, these must both be positive charges.

→  has a greater radius than , so ’s charge to mass ratio is greater than ’s.

→ initially curves downwards, using the right hand palm rule, it must have a negative charge.

→ has the same radius of motion as , so the charge to mass ratios of and are the same.

→ has a smaller radius than , so ’s charge to mass ratio is less than that of .


Mean mark 60%.

PHYSICS, M6 2020 HSC 19 MC

A conductor is in a uniform magnetic field. The conductor rotates around the end at a constant angular velocity.
 

Which graph shows the induced emf between and as the conductor completes one revolution from the position shown?
 

 

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Show Worked Solution

At the starting position shown, electrons in the rod are moving to the right, parallel to the magnetic field lines. So, there is no force acting on the.

→ EMF of zero.

After a quarter of a rotation, electrons in the rod are moving up the page. Using the right hand palm rule, they experience a force out of the page. This will not induce an EMF between and

→ the graph will show an EMF of zero at both and after a quarter of a rotation.


♦♦ Mean mark 10%.