Motion In Electromagnetic Fields

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शिक्षकों के लिए: Motion In Electromagnetic Fields (Physics, HL) के लिए इस्तेमाल के लिए तैयार लेसन स्लाइड्स, रिवीज़न नोट्स — इन्हें अपने लेसन में इस्तेमाल करें, या टॉपिक को एक इंटरैक्टिव क्लास एक्टिविटी की तरह चलाएं जिसे आपके शिक्षार्थी लाइव गेम की तरह खेलें।

लेसन नोट्स

Magnetic Force on a Current-Carrying Conductor

A current-carrying conductor produces its own magnetic field and experiences a force when placed in an external magnetic field.
The force F on a conductor of length L carrying current I at an angle θ to a magnetic field of flux density B is given by F = BIL sin θ.
The force is maximum when the conductor is perpendicular to the field (θ = 90°, sin θ = 1), giving F = BIL.
The force is zero when the conductor is parallel to the field (θ = 0°, sin θ = 0).
The force can be increased by increasing the magnetic field strength, the current, or the length of the conductor within the field.
The direction of the force is given by Fleming's left-hand rule: thumb = force (motion), first finger = magnetic field, second finger = conventional current.
In three dimensions, dots represent a magnetic field directed out of the page and crosses represent a field directed into the page.

Setup for demonstrating the force on a current-carrying conductor in a magnetic field.

Magnetic Force between Two Parallel Conductors

A current-carrying conductor produces a magnetic field around it; the direction is given by the right-hand thumb rule.
Two parallel conductors attract each other if their currents flow in the same direction and repel if the currents are in opposite directions.
The force per unit length between two parallel conductors is F/L = (μ₀ I₁ I₂) / (2π r), where r is the separation between them.
μ₀ is the magnetic permeability of free space, equal to 4π × 10⁻⁷ N A⁻².
The forces on each wire are equal in magnitude and opposite in direction, consistent with Newton's third law.

Magnetic Force on a Moving Charge

A moving charge produces its own magnetic field and experiences a force when interacting with an external magnetic field.
The force F on a charge q moving with speed v at an angle θ to a magnetic field B is F = Bqv sin θ.
The force is maximum when the charge moves perpendicular to the field (θ = 90°), giving F = Bqv.
A charge moving parallel to the magnetic field experiences no magnetic force.
The direction of the force is found using Fleming's left-hand rule, with the second finger pointing in the direction of conventional current (opposite to the motion of a negative charge).
The force is always perpendicular to both the velocity and the magnetic field.

Charged Particles in Magnetic Fields

A charged particle moving perpendicular to a uniform magnetic field follows a circular path because the magnetic force is always perpendicular to its velocity.
The magnetic force provides the centripetal force, so mv²/r = BQv.
Rearranging gives the radius of the path: r = mv / (BQ).
The radius is larger for faster particles (r ∝ v) and more massive particles (r ∝ m).
The radius is smaller for particles with greater charge (r ∝ 1/q) and in stronger magnetic fields (r ∝ 1/B).
The centripetal acceleration is in the same direction as the magnetic force, given by Newton's second law F = ma.

Magnetic field lines

Charged Particles in Electric Fields

A charged particle in a uniform electric field experiences a constant electric force F = EQ.
A stationary charged particle will move parallel to the electric field lines (along or against depending on its charge).
A charged particle moving through a uniform electric field follows a parabolic trajectory.
A positive charge is deflected towards the negative plate; a negative charge is deflected towards the positive plate.
The amount of deflection depends on the particle's mass (greater mass → smaller deflection), charge (greater charge → greater deflection), and speed (greater speed → smaller deflection).
An uncharged particle, such as a neutron, experiences no force and travels straight through undeflected.

Attraction and repulsion of charge

Charged Particles in Electric and Magnetic Fields

A charged particle moving in perpendicular uniform electric and magnetic fields experiences a force parallel to the electric field and a force perpendicular to the magnetic field.
For a positively charged particle, the electric force acts in the direction of the electric field, while the magnetic force acts in the opposite direction.
For a negatively charged particle, the electric force acts opposite to the electric field, while the magnetic force acts in the opposite direction to that on a positive charge.
When the electric and magnetic forces are equal in magnitude and opposite in direction, the particle moves in a straight line with constant speed.
Equating the forces qE = Bqv gives the speed v = E/B.
This principle is used in velocity selectors and in J.J. Thomson's experiment to determine the charge-to-mass ratio of an electron.

Charge-to-Mass Ratio

The charge-to-mass ratio is defined as Q/m.
For an electron, e/mₑ = 1.76 × 10¹¹ C kg⁻¹; for a proton, e/mₚ = 9.58 × 10⁷ C kg⁻¹.
The charge-to-mass ratio can be determined by investigating the path of a charged particle in a uniform magnetic field.
J.J. Thomson used Helmholtz coils to produce a uniform magnetic field and oppositely charged parallel plates to produce a uniform electric field.
When the electric and magnetic forces balance, the beam is straight and the speed is v = V / (Bd).
With the electric field off, the particle moves in a circular path of radius r = mv / (Bq).
Combining these gives the charge-to-mass ratio: q/m = V / (r B² d).

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साइन अप करें — फ्री लॉग इन

प्रैक्टिस सवाल

फ्री प्रीव्यू — 63 में से 8 सवाल। सभी देखने के लिए साइन अप करें।

1.A straight wire carrying current I is placed in a uniform magnetic field of flux density B. The force on the wire is given by F = BIL sin θ. What does θ represent in this equation?
Easy
- AThe angle between the wire and the magnetic field
- BThe angle between the current and the magnetic force
- CThe angle between the wire and the horizontal
- DThe angle between the magnetic field and the magnetic force
2.Which of the following is the fundamental SI unit of magnetic flux density?
Easy
- ATesla (T)
- BWeber (Wb)
- CNewton (N)
- DAmpere (A)
3.A wire of length 0.50 m carries a current of 2.0 A and is placed at 30° to a uniform magnetic field of flux density 0.10 T. What is the magnitude of the force on the wire?
Medium
- A0.050 N
- B0.10 N
- C0.025 N
- D0.43 N
4.A charged particle moves with speed v perpendicular to a uniform magnetic field B. The magnetic force on the particle is given by F = Bqv. Which of the following changes would double the magnetic force?
Easy
- ADoubling the speed of the particle
- BDoubling the mass of the particle
- CDoubling the charge of the particle and halving its speed
- DHalving the magnetic flux density
5.An electron enters a uniform magnetic field directed into the page, moving from left to right. In which direction does the magnetic force on the electron act?
Medium
- AUpwards
- BDownwards
- CInto the page
- DOut of the page
6.A charged particle moves in a circular path of radius r in a uniform magnetic field B. The radius is given by r = mv/(Bq). Which of the following will increase the radius of the path?
Medium
- AIncreasing the mass of the particle
- BIncreasing the magnetic flux density
- CIncreasing the charge of the particle
- DDecreasing the speed of the particle
7.Which of the following statements about the magnetic force on a current-carrying conductor are correct? (Select all that apply.)
Medium
- AThe force is maximum when the conductor is perpendicular to the magnetic field.
- BThe force is zero when the conductor is parallel to the magnetic field.
- CThe force is always in the same direction as the magnetic field.
- DThe force can be increased by increasing the current in the conductor.
- EThe force depends on the length of the conductor within the field.
8.A charged particle moves through a region where uniform electric and magnetic fields are perpendicular to each other and to the particle's velocity. The particle travels undeflected. Which of the following statements are correct? (Select all that apply.)
Medium
- AThe electric force and magnetic force are equal in magnitude.
- BThe electric force and magnetic force act in opposite directions.
- CThe speed of the particle is given by v = E/B.
- DThe particle must be uncharged.
- EThe particle's path is circular.

और सवाल

9.A current-carrying conductor experiences no magnetic force when it is parallel to an external magnetic field.
Easy
True or false?
10.Two parallel wires carrying currents in the same direction repel each other.
Easy
True or false?
11.In a uniform magnetic field, a charged particle moving perpendicular to the field travels in a circular path with constant speed.
Medium
True or false?
12.Match each quantity in the equation F = Bqv to its correct SI unit.
Medium
- Force (F)
- Magnetic flux density (B)
- Charge (q)
- Speed (v)
- N
- T
- C
- m s^-1
13.Arrange the steps to derive the radius r of a charged particle moving perpendicular to a uniform magnetic field.
Medium
- Equate centripetal force mv²/r to magnetic force Bqv
- Cancel one factor of v from both sides
- Rearrange to make r the subject
- Write r = mv/(Bq)
14.If the wire is rotated so that it is parallel to the magnetic field, what is the new force on the wire?
Medium
- A0 N
- B0.30 N
- C0.60 N
- D1.2 N
15.A current-carrying conductor is placed in a uniform magnetic field. Which of the following changes will increase the magnitude of the magnetic force on the conductor? (Select all that apply.)
Medium
- AIncreasing the current in the conductor
- BIncreasing the strength of the magnetic field
- CIncreasing the length of the conductor within the field
- DRotating the conductor so it becomes parallel to the field
- EDecreasing the angle between the conductor and the field from 90° to 30°
16.A charged particle moves in a uniform magnetic field. Which of the following statements are correct? (Select all that apply.)
Medium
- AThe magnetic force is always perpendicular to the particle's velocity.
- BThe magnetic force does no work on the particle.
- CThe speed of the particle remains constant.
- DThe particle travels in a circular path if its velocity is perpendicular to the field.
- EThe magnetic force is maximum when the particle moves parallel to the field.
17.An electron enters a uniform magnetic field directed into the page, moving from left to right. Which of the following statements about the force on the electron are correct? (Select all that apply.)
Hard
- AThe force is directed upwards.
- BThe force is directed downwards.
- CThe force is perpendicular to the electron's velocity.
- DThe force is parallel to the magnetic field.
- EThe force acts as a centripetal force, causing circular motion.
18.Two long, straight parallel wires carry currents in opposite directions. Which of the following statements are correct? (Select all that apply.)
Medium
- AThe wires repel each other.
- BThe wires attract each other.
- CThe magnetic field lines between the wires reinforce each other.
- DThe force per unit length is proportional to the product of the currents.
- EThe force per unit length is inversely proportional to the separation between the wires.
19.A charged particle moves through a region where uniform electric and magnetic fields are perpendicular to each other and to the particle's velocity. The particle travels in a straight line with constant speed. Which of the following are true? (Select all that apply.)
Medium
- AThe electric force and magnetic force are equal in magnitude.
- BThe electric force and magnetic force are opposite in direction.
- CThe speed of the particle is given by v = E/B.
- DThe particle must be positively charged.
- EThe net force on the particle is zero.
20.A charged particle moves in a circular path of radius r in a uniform magnetic field B. Which of the following changes will increase r? (Select all that apply.)
Hard
- AIncreasing the particle's speed v
- BIncreasing the particle's mass m
- CIncreasing the magnetic flux density B
- DDecreasing the particle's charge q
- EDecreasing the particle's speed v
21.A charged particle enters a uniform electric field between two parallel charged plates. Which of the following statements about its motion are correct? (Select all that apply.)
Hard
- AThe particle experiences a constant electric force.
- BThe particle follows a parabolic path.
- CA positive particle is deflected towards the negative plate.
- DThe deflection is greater for a particle with greater mass.
- EThe deflection is greater for a particle with greater speed.
22.Match each quantity in the equation F = BIL sin θ to its correct SI unit.
Medium
- F
- B
- I
- L
- N
- T
- A
- m
23.Match each particle property to the effect it has on the radius r of its circular path in a uniform magnetic field.
Medium
- Increasing speed v
- Increasing mass m
- Increasing charge q
- Increasing magnetic flux density B
- r increases
- r decreases
24.Match each term to its correct definition or description.
Medium
- Magnetic flux density
- Fleming's left-hand rule
- Right-hand thumb rule
- Charge-to-mass ratio
- The force per unit current per unit length on a conductor perpendicular to a magnetic field
- A rule to find the direction of the force on a current-carrying conductor in a magnetic field
- A rule to find the direction of the magnetic field around a current-carrying wire
- The ratio of a particle's charge to its mass
25.Arrange the steps to determine the direction of the force on a current-carrying conductor using Fleming's left-hand rule.
Medium
- Point the first finger in the direction of the magnetic field B
- Point the second finger in the direction of the conventional current I
- Point the thumb in the direction of the force F
- Hold the thumb, first finger and second finger mutually perpendicular
26.Arrange the steps to calculate the charge-to-mass ratio of an electron using perpendicular electric and magnetic fields.
Hard
- Measure the radius r of the circular path when only the magnetic field acts
- Equate the electric and magnetic forces to find the speed: v = V/(Bd)
- Calculate the charge-to-mass ratio using q/m = v/(rB)
- Adjust the electric field until the electron beam is undeflected
27.The magnetic force on a current-carrying conductor is maximum when the conductor is perpendicular to the magnetic field.
Easy
True or false?
28.A charged particle moving parallel to a uniform magnetic field experiences a magnetic force.
Easy
True or false?
29.Two parallel wires carrying currents in the same direction attract each other.
Medium
True or false?
30.In a region of perpendicular uniform electric and magnetic fields, a charged particle moving with speed v = E/B experiences a net force.
Medium
True or false?
31.A straight wire of length 0.60 m carrying a current of 3.0 A is placed in a uniform magnetic field of flux density 0.20 T. The angle between the wire and the field is 40°. What is the magnitude of the force on the wire?
Medium
- A0.23 N
- B0.36 N
- C0.29 N
- D0.18 N
32.A proton moves at 2.5 × 10⁶ m s^-1 perpendicular to a uniform magnetic field of flux density 0.15 T. Calculate the radius of its circular path. (Proton mass = 1.67 × 10^-27 kg, charge = 1.60 × 10^-19 C)
Medium
- A0.17 m
- B0.087 m
- C0.34 m
- D0.52 m
33.The magnetic force on a current-carrying conductor is maximum when the conductor is parallel to the magnetic field.
Easy
True or false?
34.Match each quantity with its correct SI unit.
Medium
- Magnetic flux density B
- Force F
- Current I
- Charge q
- Tesla (T)
- Newton (N)
- Ampere (A)
- Coulomb (C)
35.Arrange the steps to determine the direction of the force on a charged particle moving in a magnetic field using Fleming's left-hand rule.
Medium
- Point the first finger in the direction of the magnetic field B.
- Point the second finger in the direction of conventional current (opposite to electron motion if negative).
- The thumb points in the direction of the force F.
- Ensure the thumb, first finger and second finger are mutually perpendicular.
36.A beam of electrons enters a uniform magnetic field directed into the page, moving from left to right. In which direction does the magnetic force on the electrons act?
Hard
- AUpwards
- BDownwards
- CInto the page
- DOut of the page
37.An electron enters a region with perpendicular uniform electric and magnetic fields and travels undeflected. The electric field strength is 2.0 × 10⁴ V m^-1 and the magnetic flux density is 0.10 T. What is the speed of the electron?
Hard
- A2.0 × 10⁵ m s^-1
- B2.0 × 10³ m s^-1
- C2.0 × 10⁶ m s^-1
- D2.0 × 10⁴ m s^-1
38.A copper rod is placed in a uniform magnetic field and connected to a circuit. When the switch is closed, the rod accelerates in the direction of the magnetic force. Which change would cause the rod to accelerate in the opposite direction?
Medium
- AReversing the direction of the current in the rod
- BIncreasing the current in the rod
- CIncreasing the magnetic flux density of the field
- DRotating the rod so it is parallel to the magnetic field
39.In an experiment, a charged particle enters a region of uniform magnetic field and follows a circular path. The radius of the path is measured for different speeds of the particle while the magnetic flux density is kept constant. Which graph would be a straight line through the origin?
Hard
- ARadius r against speed v
- BRadius r against 1/speed v
- CRadius r against speed squared v²
- DRadius r against 1/speed squared 1/v²
40.A beam of electrons is fired into a uniform magnetic field directed into the page, moving from left to right. The beam curves upwards. What is the direction of the magnetic field?
Medium
- AInto the page
- BOut of the page
- CTo the right
- DTo the left
41.State the name of the rule used to determine the direction of the force on a current-carrying conductor in a magnetic field.
Easy
42.What is the name of the device that uses perpendicular electric and magnetic fields to determine the charge-to-mass ratio of an electron?
Medium
43.A wire of length 1.2 m carries a current of 0.85 A and is placed at 30° to a magnetic field of flux density 70 mT. Calculate the force on the wire in newtons.
Medium
44.An electron travels at 3.0 × 10⁶ m s^-1 perpendicular to a uniform magnetic field of flux density 5.6 mT. Calculate the radius of its circular path in metres. (Electron charge-to-mass ratio e/m = 1.76 × 10¹¹ C kg^-1.)
Medium
45.Complete the sentence about the force on a current-carrying conductor.
Easy
The force on a current-carrying conductor in a magnetic field is given by F = BIL ____, where θ is the angle between the conductor and the magnetic field.
46.Name the three quantities that, when increased, will increase the magnetic force on a current-carrying conductor in a magnetic field.
Medium
The force can be increased by increasing the magnetic flux density, the ____, and the ____.
47.Calculate the magnitude of the force on the wire in newtons.
Medium
48.A wire of length 0.80 m carries a current of 1.5 A and is placed at 90° to a uniform magnetic field of flux density 0.25 T. Calculate the magnitude of the force on the wire in newtons.
Medium
49.An electron travels at 2.5 × 10⁶ m s⁻¹ perpendicular to a uniform magnetic field of flux density 0.40 T. Calculate the radius of its circular path in metres. (Electron mass = 9.11 × 10⁻³¹ kg, charge = 1.60 × 10⁻¹⁹ C)
Hard
50.An electron moves through a region where uniform electric and magnetic fields are perpendicular to each other and to its velocity. The electric field strength is 1.2 × 10⁴ N C⁻¹ and the magnetic flux density is 0.040 T. Calculate the speed of the electron in m s⁻¹ if it travels undeflected.
Hard
51.Complete the sentence about the magnetic force on a moving charge.
Medium
When a charged particle moves perpendicular to a uniform magnetic field, the magnetic force provides the ____ force, causing the particle to move in a circular path.
52.Complete the sentence about the force between two parallel current-carrying conductors.
Medium
Two parallel wires carrying currents in the ____ direction attract each other, while currents in the ____ direction repel each other.
53.State and explain whether the speed of a proton at point P is the same as its speed at point Q after travelling through a uniform magnetic field in a quarter circle.
Hard
54.Outline why a charged particle moving perpendicular to a uniform magnetic field follows a circular path.
Hard
55.Explain why a charged particle moving perpendicular to a uniform magnetic field follows a circular path.
Hard
56.Explain how the charge-to-mass ratio of an electron can be determined using perpendicular electric and magnetic fields.
Challenge
57.State and explain whether the speed of the proton at P is the same as its speed at Q.
Hard
58.A wire of length 1.2 m carries a current of 0.85 A and is placed at 30° to a magnetic field of flux density 70 mT. Calculate the force on the wire in newtons.
Medium
- A-0.964 N
- B2.036 N
- C0.036 N
- D1.036 N
59.An electron travels at 3.0 × 10⁶ m s^-1 perpendicular to a uniform magnetic field of flux density 5.6 mT. Calculate the radius of its circular path in metres. (Electron charge-to-mass ratio e/m = 1.76 × 10¹¹ C kg^-1.)
Medium
- A0.003 m
- B-0.997 m
- C2.003 m
- D1.003 m
60.Calculate the magnitude of the force on the wire in newtons.
Medium
- A-0.4 N
- B2.6 N
- C0.6 N
- D1.6 N
61.A wire of length 0.80 m carries a current of 1.5 A and is placed at 90° to a uniform magnetic field of flux density 0.25 T. Calculate the magnitude of the force on the wire in newtons.
Medium
- A2.3 N
- B-0.7 N
- C1.3 N
- D0.3 N
62.An electron travels at 2.5 × 10⁶ m s⁻¹ perpendicular to a uniform magnetic field of flux density 0.40 T. Calculate the radius of its circular path in metres. (Electron mass = 9.11 × 10⁻³¹ kg, charge = 1.60 × 10⁻¹⁹ C)
Hard
- A2 m
- B-1 m
- C1 m
- D0.0000356 m
63.An electron moves through a region where uniform electric and magnetic fields are perpendicular to each other and to its velocity. The electric field strength is 1.2 × 10⁴ N C⁻¹ and the magnetic flux density is 0.040 T. Calculate the speed of the electron in m s⁻¹ if it travels undeflected.
Hard
- A360000 m/s
- B300000 m/s
- C270000 m/s
- D330000 m/s

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