Motion In Electromagnetic Fields

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수업 노트

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 is given by F = BIL sin θ, where B is magnetic flux density, I is current, L is the length of conductor in the field, and θ is the angle between the conductor and the B field.
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 in 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.

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

Representing Magnetic Fields in 3D

Dots (or circles with dots) represent a magnetic field directed out of the page.
Crosses represent a magnetic field directed into the page.
Remember: an arrow approaching head-on shows only its tip (dot); an arrow receding shows the cross of its feathers (cross).
Conventional current flows from positive to negative, opposite to the direction of electron flow.

Magnetic field lines

Magnetic Force between Two Parallel Conductors

Each current-carrying conductor produces a magnetic field around it, determined by the right-hand thumb rule.
Parallel conductors with currents in the same direction attract each other.
Parallel conductors with currents in opposite directions repel each other.
The force per unit length between two parallel conductors is F/L = μ₀I₁I₂ / (2πr), where r is the separation and μ₀ = 4π × 10⁻⁷ N A⁻².
The forces on the two wires are equal and opposite (Newton's third law).

Magnetic Force on a Moving Charge

A moving charge produces its own magnetic field and experiences a force when in an external magnetic field.
The force is given by F = Bqv sin θ, where q is the charge, v is the speed, and θ is the angle between velocity and the B field.
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 force.
The force is always perpendicular to both the velocity and the magnetic field.
For a negative charge, the direction of conventional current is opposite to its motion; use Fleming's left-hand rule with the current direction.

Charged Particles in Magnetic Fields

A charged particle moving perpendicular to a uniform magnetic field travels in a circular path because the magnetic force is always perpendicular to its velocity.
The magnetic force provides the centripetal force: mv²/r = BQv.
Rearranging gives the radius of the path: r = mv / (BQ).
The radius increases with greater mass or speed, and decreases with greater charge or magnetic field strength.
The centripetal acceleration is in the same direction as the magnetic force (Newton's second law, F = ma).

Charged Particles in Electric Fields

A charged particle in a uniform electric field experiences a constant force and travels in a parabolic trajectory.
A positive charge is deflected towards the negative plate; a negative charge towards the positive plate.
An uncharged particle (e.g. a neutron) experiences no force and travels straight through.
The amount of deflection depends on mass (greater mass → smaller deflection), charge (greater charge → greater deflection), and speed (greater speed → smaller deflection).

Attraction and repulsion of charge

Charged Particles in Electric & Magnetic Fields

When electric and magnetic fields are perpendicular, a charged particle experiences an electric force parallel to E and a magnetic force perpendicular to B.
For a positively charged particle, the electric and magnetic forces act in opposite directions; the same is true for a negatively charged particle, but with directions reversed.
When the electric and magnetic forces are equal in magnitude, the particle moves in a straight line with constant speed.
Equating the forces: qE = Bqv, which 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.
J.J. Thomson used Helmholtz coils (uniform B field) and oppositely charged parallel plates (uniform E field) to determine e/mₑ.
The speed of particles is found using perpendicular electric and magnetic fields: v = V / (Bd).
The charge-to-mass ratio is then q/m = V / (rB²d), where r is the radius of the circular path when the electric field is switched off.

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연습 문제

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1.What does the magnetic flux density B represent?
Easy
- AThe force per unit current per unit length on a conductor perpendicular to the field
- BThe total magnetic force on a stationary charge
- CThe magnetic field strength measured in volts per metre
- DThe force per unit charge on a stationary charge
2.A straight wire of length 0.90 m carries a current of 1.5 A and is placed at 45° to a uniform magnetic field of flux density 0.20 T. What is the magnitude of the force on the wire?
Medium
- A0.19 N
- B0.27 N
- C0.38 N
- D0.14 N
3.Which of the following changes would increase the magnitude of the force on a current-carrying wire in a magnetic field? (select all that apply)
Medium
- AIncreasing the current in the wire
- BIncreasing the magnetic flux density
- CIncreasing the length of wire within the field
- DRotating the wire so it is parallel to the field
- EReversing the direction of the current
4.A current-carrying conductor experiences no magnetic force when it is placed:
Easy
- Aat 90° to the magnetic field
- Bparallel to the magnetic field
- Cat 45° to the magnetic field
- Dperpendicular to the magnetic field
5.Which of the following is the fundamental SI unit of magnetic flux density?
Easy
- ATesla (T)
- BWeber (Wb)
- CNewton per ampere (N A⁻¹)
- DVolt (V)
6.Two parallel wires carrying currents in the same direction attract each other.
Easy
True or false?
7.A charged particle moving parallel to a uniform magnetic field experiences a magnetic force.
Easy
True or false?
8.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

더 많은 문제

9.A proton and an electron enter the same uniform magnetic field with the same speed perpendicular to the field. Which particle follows a circular path with the larger radius?
Medium
- AThe proton, because it has greater mass
- BThe electron, because it has smaller mass
- CBoth have the same radius because they have the same speed
- DThe electron, because it has greater charge-to-mass ratio
10.A charged particle moves in a circular path of radius r in a uniform magnetic field. Which of the following changes would increase the radius of the path?
Medium
- AIncreasing the magnetic flux density B
- BIncreasing the charge q of the particle
- CIncreasing the speed v of the particle
- DDecreasing the mass m of the particle
11.Which of the following statements about a charged particle moving in a uniform magnetic field are true? (select all that apply)
Medium
- AThe magnetic force is always perpendicular to the velocity
- BThe speed of the particle remains constant
- CThe path is circular if the velocity is perpendicular to the field
- DThe magnetic force does work on the particle
- EThe particle's kinetic energy increases
12.A proton enters a region of uniform magnetic field and follows a quarter-circular path. Which of the following is correct about its motion?
Medium
- AIts speed at the exit is the same as at the entry
- BIts speed increases because of the magnetic force
- CIts speed decreases because of the magnetic force
- DIts speed depends on the radius of the path
13.A charged particle enters a uniform electric field between two parallel plates and moves perpendicular to the field lines. What is the shape of its path?
Medium
- ACircular
- BParabolic
- CStraight line
- DElliptical
14.Which factors affect the amount of deflection of a charged particle moving through a uniform electric field? (select all that apply)
Medium
- AThe mass of the particle
- BThe magnitude of the charge on the particle
- CThe speed of the particle
- DThe electric field strength
- EThe magnetic flux density
15.In a velocity selector, a charged particle moves undeflected through perpendicular electric and magnetic fields. What is the speed of the particle?
Medium
- Av = E / B
- Bv = B / E
- Cv = E × B
- Dv = B / (E q)
16.Match each quantity to its correct SI unit.
Medium
- Magnetic flux density
- Force
- Current
- Charge
- Tesla (T)
- Newton (N)
- Ampere (A)
- Coulomb (C)
17.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
- Point the second finger in the direction of the conventional current
- Point the thumb in the direction of the force
- Ensure all three fingers are mutually perpendicular
18.A current-carrying conductor placed parallel to an external magnetic field experiences the maximum magnetic force.
Easy
True or false?
19.A current-carrying wire is placed at an angle θ to a uniform magnetic field. At which value of θ is the force on the wire a maximum?
Easy
- A0°
- B45°
- C90°
- D180°
20.A current-carrying wire is placed parallel to a uniform magnetic field. What is the magnitude of the magnetic force on the wire?
Easy
- ABIL
- B0.5 BIL
- CZero
- D2 BIL
21.A wire of length 15 cm carries a current of 2.0 A and 'floats' in equilibrium in a uniform magnetic field. The wire has a mass of 30 g. What is the magnitude of the magnetic force acting on the wire? (Take g = 9.8 m s⁻²)
Medium
- A0.15 N
- B0.29 N
- C0.45 N
- D2.9 N
22.A charged particle moves in a uniform magnetic field. Which of the following statements are true? (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 particle's speed remains constant.
- DThe particle's kinetic energy increases.
- EThe magnetic force is parallel to the velocity.
23.Which of the following changes would increase the radius of the circular path of a charged particle moving in a uniform magnetic field? (select all that apply)
Medium
- AIncreasing the particle's speed
- BIncreasing the particle's mass
- CIncreasing the magnetic flux density
- DIncreasing the particle's charge
- EDecreasing the magnetic flux density
24.A charged particle enters a uniform electric field between two parallel plates, moving perpendicular to the field lines. What is the shape of its path?
Medium
- ACircular
- BParabolic
- CStraight
- DElliptical
25.An electron enters a region of uniform electric field between two parallel plates. Compared with a proton entering with the same velocity, how is the electron deflected?
Medium
- AIn the same direction, with the same deflection
- BIn the opposite direction, with a much larger deflection
- CIn the opposite direction, with a much smaller deflection
- DNot deflected at all
26.Two long parallel wires carry currents in opposite directions. What is the nature of the force between them?
Medium
- AAttractive
- BRepulsive
- CZero
- DDepends on the magnitude of the currents
27.Two long parallel wires carry currents I₁ and I₂ and are separated by a distance r. The force per unit length between them is given by which expression?
Medium
- Aμ₀ I₁ I₂ / (2π r)
- Bμ₀ I₁ I₂ / (4π r)
- Cμ₀ I₁ I₂ r / (2π)
- D2π μ₀ I₁ I₂ / r
28.Which of the following are true about the motion of a charged particle in a uniform magnetic field? (select all that apply)
Hard
- AThe particle's kinetic energy remains constant.
- BThe magnetic force acts as a centripetal force.
- CThe particle's speed increases as it curves.
- DThe magnetic force is perpendicular to the velocity.
- EThe particle's path is a straight line.
29.What is the fundamental SI unit of magnetic flux density?
Medium
- Akg A⁻¹ s⁻²
- Bkg A s⁻²
- Ckg m A⁻¹ s⁻²
- Dkg m² A⁻¹ s⁻²
30.Arrange the steps to determine the direction of the magnetic force on a moving negative charge using Fleming's left-hand rule.
Medium
- Point the first finger in the direction of the magnetic field.
- Point the second finger in the direction opposite to the particle's velocity.
- Point the thumb in the direction of the magnetic force.
- Ensure the thumb, first finger and second finger are mutually perpendicular.
31.Match each particle property to its effect on the radius of the circular path in a uniform magnetic field.
Medium
- Speed v
- Mass m
- Charge q
- Flux density B
- r ∝ v
- r ∝ m
- r ∝ 1/q
- r ∝ 1/B
32.Which of the following changes would decrease the radius of the circular path of a charged particle in a uniform magnetic field? (select all that apply)
Medium
- AIncreasing the magnetic flux density
- BIncreasing the particle's charge
- CIncreasing the particle's speed
- DIncreasing the particle's mass
- EDecreasing the magnetic flux density
33.A beam of electrons enters a uniform magnetic field directed into the page, moving from right to left. In which direction does the magnetic force on the electrons act?
Medium
- AUpwards
- BDownwards
- CInto the page
- DOut of the page
34.A charged particle moves in a circular path of radius r in a uniform magnetic field. If the speed of the particle is doubled while the magnetic field is halved, how does the radius change?
Hard
- AIt is halved
- BIt is unchanged
- CIt is doubled
- DIt is quadrupled
35.In a uniform electric field, a charged particle at rest is released. How does it move?
Medium
- AIt moves in a circle.
- BIt moves along the electric field lines.
- CIt moves perpendicular to the field lines.
- DIt remains stationary.
36.Which of the following factors affect the amount of deflection of a charged particle moving through a uniform electric field? (select all that apply)
Medium
- AThe particle's mass
- BThe particle's charge
- CThe particle's speed
- DThe particle's colour
- EThe particle's temperature
37.In a uniform magnetic field, the magnetic force on a charged particle is always perpendicular to the particle's velocity.
Easy
True or false?
38.An electron and a proton enter a uniform magnetic field with the same speed, perpendicular to the field. Which particle has the larger radius of circular path, and why?
Hard
- AThe electron, because it has a smaller charge
- BThe proton, because it has a larger mass
- CThe electron, because it has a larger mass
- DThe proton, because it has a larger charge
39.Which of the following statements about a charged particle in crossed electric and magnetic fields (velocity selector) are true? (select all that apply)
Hard
- AThe electric and magnetic forces act in opposite directions.
- BThe particle moves in a straight line when the forces balance.
- CThe speed of the particle is given by v = E / B.
- DThe particle's speed increases as it passes through.
- EThe forces act in the same direction.
40.A copper rod of length 0.25 m is placed in a uniform magnetic field of flux density 0.40 T. The rod carries a current of 2.0 A and is at 60° to the field. What is the magnitude of the force on the rod?
Medium
- A0.17 N
- B0.20 N
- C0.35 N
- D0.40 N
41.A straight 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. Give your answer in newtons to 2 significant figures.
Medium
42.An electron travels at 4.8 × 10⁷ m s⁻¹ perpendicular to a uniform magnetic field of flux density 0.5 T. Calculate the magnitude of the magnetic force on the electron. Give your answer in newtons to 2 significant figures.
Medium
43.An electron travels at right angles to a uniform magnetic field of flux density 5.6 mT. The speed of the electron is 3.0 × 10⁶ m s⁻¹. Calculate the radius of the circular orbit of the electron. Give your answer in metres to 2 significant figures.
Medium
44.Complete the sentence about Fleming's left-hand rule.
Easy
In Fleming's left-hand rule, the thumb points in the direction of the ____, the first finger points in the direction of the ____, and the second finger points in the direction of the ____.
45.Complete the sentence about representing magnetic fields in 3D.
Easy
In diagrams, dots represent a magnetic field directed ____ the page, and crosses represent a magnetic field directed ____ the page.
46.Complete the sentence about charged particles in electric fields.
Medium
In a uniform electric field, a stationary charged particle will move ____ to the electric field lines, while a moving charged particle will follow a ____ trajectory.
47.Name the device that accelerates charged particles along a spiral path.
Easy
48.What is the name of the rule used to determine the direction of the force on a current-carrying conductor in a magnetic field?
Medium
49.Using the data from the previous question (wire length 15 cm, current 2.0 A, mass 30 g), calculate the magnetic flux density required to keep the wire floating in equilibrium. Give your answer in tesla.
Medium
50.A 25.0 m length of wire carries a current of 2000 A. The Earth's magnetic field at the wire's position is 4.50 × 10⁻⁵ T and makes an angle of 45° with the wire. Calculate the force experienced by this length of wire. Give your answer in newtons.
Medium
51.Complete the sentence about the force on a current-carrying conductor in a magnetic field.
Medium
The force on a current-carrying conductor is given by F = BIL sin θ, where θ is the angle between the ____ and the ____.
52.An electron travels at 4.8 × 10⁷ m s⁻¹ perpendicular to a uniform magnetic field of flux density 0.5 T. Calculate the magnitude of the magnetic force on the electron. Give your answer in newtons.
Medium
53.State and explain whether the speed of a proton at point P is the same as the speed at point Q after it has travelled through a uniform magnetic field.
Hard
54.Explain why a charged particle moving perpendicular to a uniform magnetic field follows a circular path.
Hard
55.State and explain whether a charged particle is positively or negatively charged when it enters a region of magnetic field directed into the page and follows a quarter-circle path curving upwards.
Hard
56.Outline what is meant by magnetic flux density.
Hard
57.State two changes that would increase the radius of the circular path of a charged particle in a magnetic field.
Hard
58.A straight 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. Give your answer in newtons to 2 significant figures.
Medium
- A-0.964 N
- B1.036 N
- C0.036 N
- D2.036 N
59.An electron travels at 4.8 × 10⁷ m s⁻¹ perpendicular to a uniform magnetic field of flux density 0.5 T. Calculate the magnitude of the magnetic force on the electron. Give your answer in newtons to 2 significant figures.
Medium
- A3.8e-12 N
- B-1 N
- C1 N
- D2 N
60.An electron travels at right angles to a uniform magnetic field of flux density 5.6 mT. The speed of the electron is 3.0 × 10⁶ m s⁻¹. Calculate the radius of the circular orbit of the electron. Give your answer in metres to 2 significant figures.
Medium
- A1.003 m
- B-0.997 m
- C0.003 m
- D2.003 m
61.Using the data from the previous question (wire length 15 cm, current 2.0 A, mass 30 g), calculate the magnetic flux density required to keep the wire floating in equilibrium. Give your answer in tesla.
Medium
- A2.98 T
- B-0.02 T
- C0.98 T
- D1.98 T
62.A 25.0 m length of wire carries a current of 2000 A. The Earth's magnetic field at the wire's position is 4.50 × 10⁻⁵ T and makes an angle of 45° with the wire. Calculate the force experienced by this length of wire. Give your answer in newtons.
Medium
- A3.59 N
- B0.59 N
- C2.59 N
- D1.59 N
63.An electron travels at 4.8 × 10⁷ m s⁻¹ perpendicular to a uniform magnetic field of flux density 0.5 T. Calculate the magnitude of the magnetic force on the electron. Give your answer in newtons.
Medium
- A3.84e-12 N
- B-1 N
- C1 N
- D2 N

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