Unit 4.2 Magnetic Fields
What is the equation for the force on a charged particle in a magnetic field and how do you derive it
- The force on a current carrying wire is given by F = BIl sinθ - Electric current, I, is the flow of charge, Q, over time so I = Q/t - A charged particle which moves a distance l in time t has a velocity, v = l/t, so l = vt Putting all these equations together gives the force on a charged particle in a magnetic field: F = B x Q/t x vt x sinθ SO: F = Bqv sinθ F = force (N) B = Magnetic Flux density (T) q = charge on the particle (C) v = velocity of particle (ms-1) θ = angle between current and magnetic field
How does a wire carrying a current in an external magnetic field experience a force
1) If you put a current-carrying wire into an external magnetic field (e.g. between two magnets), the field around the wire and the field from the magnets are added together. This causes a resultant field — lines closer together show where the magnetic field is stronger. These bunched lines cause a 'pushing' force on the wire. 2) The direction of the force is always perpendicular to both the current direction and the magnetic field — it's given by Fleming's left-hand rule. 3) If the current is parallel to the field lines the size of the force is 0 N — there is no component of the magnetic field perpendicular to the current.
Magnetic field line basics
1) Magnetic fields can be represented by field lines (also called flux lines). 2) Field lines go from the north to the south pole of a magnet. 3) The closer together the lines, the stronger the field. 4) The field lines around a bar magnet, or pair of bar magnets, have a characteristic shape:
How do transformers work
1) They consist of two coils of wire wrapped around an iron core (so the iron core links them). 2) An alternating current flowing in the primary (or input) coil produces a changing magnetic field in the iron core. 3) The changing magnetic field is passed through the iron core to the secondary (or output) coil, where the changing magnetic flux induces an alternating voltage (e.m.f.) of the same frequency as the input voltage. 4) The ratio of the number of turns on each coil along with the voltage across the primary coil determines the size of the voltage induced in the secondary coil
Example A current of 1.64 A is flowing through a wire at an angle of 56° to the field lines of a uniform magnetic field. 25 cm of the wire is within the uniform field and experiences a force of 8.2 × 10-3 N. Calculate the magnetic flux density of the uniform field.
8.2 × 10-3 = B x 1.64 x 0.25 x sin56 B = 8.2 × 10-3/(1.64 x 0.25 x sin56) = 0.02412... B = 0.024 T
What happens to charged particles in a magnetic field
A force acts on a charged particle in a magnetic field. This is why a current carrying wire experiences a force in a magnetic field - electric current is the flow of negatively charged electrons
What happens to the direction of the magnetic fields when a bar magnet is dropped through a solenoid
At first, when the magnet is falling into the solenoid, the poles repel slightly, so work is done to push the magnet to the coil (e.g. N, N poles of solenoid and bar magnet) When the magnet is falling out of the solenoid, the poles attract slightly, so work is done to pull the magnet back up into the coil
Example: A 0.60 m long metal rod moves through a perpendicular uniform magnetic field with magnetic flux density 0.24 T, at a constant velocity of 0.50 ms-1. Find the flux cut by the rod in 5.0 seconds, and hence the magnitude of the e.m.f. induced.
B = 0.24T, l = 0.6m, v = 0.50 ms-1, t = 5s, A = ? Area = distance traveled x length of rod A = l x vt = 0.5 x 5 x 0.6 = 1.5 m^2 ɸ = BA ɸ = 0.24 x 1.5 = 0.36 Wb ε = 0.36/5 = 0.072 V
Example 2: Q1 An aeroplane with a wingspan of 33.9 m flies at a constant speed of 148 ms-1 perpendicular to the Earth's magnetic field, as shown. The Earth's magnetic field at the aeroplane's location is 6.00 × 10^-5 T. a) By considering how far the plane travels in 1 second, calculate the magnitude of the induced e.m.f. between the wing tips of the plane. [3 marks] b) Copy and complete the diagram to show the direction of the induced e.m.f. between the wing-tips. (Magnetic field is into the page in this diagram.)
B = 6.00 × 10^-5T, l = 33.9 m, v = 148 ms-1, t = 1s, A = ? a) A = l x vt = 33.9 x 148 x 1 = 5017 m^2 ɸ = BA ɸ = 6.00 × 10^-5 x 5017 = 0.301 Wb ε = 0.301/1 = 0.301 V b)
How can the radius of a charged particles motion in a magnetic field be found (derivation from 2 equations)
Because the charged particles follow circular motion, the force, F = Bqv also = mv^2/r So: Bqv = mv^2/r r = mv^2/BQv r = mv/BQ r = p/BQ p is the momentum of the particle (kg ms-1) B is the magnetic flux density (T) Q is the charge of the particle (C)
Example: An electron travels at a velocity of 2.00 × 10^4 ms-1 perpendicular to a uniform magnetic field with a magnetic flux density of 2.00 T. What is the magnitude of the force acting on the electron? (charge of an electron is 1.60 x 10^-19C)
F = Bqv F = 2 x 2.00 × 1.60 x 10^-19 x 10^4 F = 6.4 x 10^-15
What is the unit magnetic flux density measured in and what is the equation to find that unit
Flux density is a vector with both a direction and magnitude. It's measured in Teslas: 1 Tesla = Wb/m^2 It helps to think of flux density as the number of flux lines (measured in webers, Wb) per unit area
What is the equation of the flux linkage (Nɸ)
For a coil with N turns, perpendicular to a field Nɸ = BAN (because ɸ = BA, so N x ɸ = N x BA) The rate of change of flux linkage tells you how strong the e.m.f induced will be in volts A change in flux linkage of 1 Wb per second will induce an electromotive force of 1 volt in the loop of wire
Summary of equations Force on a wire in a magnetic field Force on a charged particle in a magnetic field Radius of a charged particles motion in a magnetic field
Force on a wire in a magnetic field F = BIl sinθ Force on a charged particle in a magnetic field F = Bqv sinq Radius of a charged particles motion in a magnetic field r = p/BQ
What happens to electrons/charged particles in a conductor when it cuts a magnetic field (What happens during electromagnetic induction)
If there is relative motion between a conducting rod and a magnetic field, the electrons in the rod will experience a force (due to FLHR) which will cause them to accumulate on one end of the rod. This means 1 end has excessive negative charge which induces an electromotive force (e.m.f./voltage/p.d.) across the ends of the rod - this is called electromagnetic induction
What does the magnetic field around a coil and solenoid look like
If you loop the wire into a coil, the field is doughnut-shaped, while a coil with length (a solenoid) forms a field like a bar magnet.
What is an alternating current
It changes the direction (back or forth) of a flow continuously (a.c.). It is used for the mains supply, because it is easier to generate and distribute, more efficient, and can be used in a transformer.
What is Flemmings Left Hand rule
It is a rule that can be used to find the direction of the resultant force on a current carrying wire in a magnetic field: The First finger points in the direction of the Field The seCond finger points in the direction of the current The Thumb points in the direction of the force REMEMBER, IT IS THE LEFT HAND NOT THE RIGHT!!!
What is the motion of charged particles in a magnetic field
The charged particles flow in a circular path due to the force acting perpendicular to the direction of motion. this means that charged particles follow circular motion. This fact is used in particle accelerators
What is the magnetic Flux density
The force on a current carrying wire at a right angle to an external magnetic field is proportional to the flux density, B. The flux density is sometimes called the strength of the magnetic field The flux density is the FORCE 1 meter of wire carrying a current of 1 A at right angles to a magnetic field will experience
Why is the induced emf in the opposite direction to the change
The idea that an induced e.m.f. will oppose the change that caused it agrees with the principle of conservation of energy - the energy used to pull a conductor through a magnetic field against the resistance caused by magnetic attraction is what produces the induced current. Lenz's law can be used to find the direction of an induced current travelling at right angles to a magnetic field
What is Lenz's Law and equation (similar)?
The induced e.m.f is always in such a direction to oppose the change that caused it. Lenz's and Farday's law can be combined to give 1 formula that works for both: ε = -change of flux linkage/time = -d(Nɸ)/dt The minus sign shows the direction of the induced emf
What is Faraday's law and equation?
The induced emf is directly proportional to the rate of change of flux linkage ε = change in flux linkage/time = d(Nɸ)/dt ε is the MAGNITUDE of the emf in volts ε increases when Nɸ increases or when t decreases
What does the size of the e.m.f. induced depend on when you move a coil in a magnetic field and what is the flux linkage
The size of the e.m.f induced depends on the magnetic flux passing through the coil , ɸ, and the number of turns in the coil, N. The product of these is called the flux linkage = Nɸ
What is the equation of the force on a wire in a magnetic field
The size of the force is proportional to the current, I, the length of the wire, l, and the magnetic flux density, B F = BIl sin θ B is magnetic flux density in Tesla (T) θ is the angle between the current and the field lines When the current is at 90 deg, sin 90 = 1, so F = BIl
What are transformers
Transformers are devices that use electromagnetic induction to change the size of the voltage for an alternating current. Step-up transformers increase the voltage by having more turns on the secondary coil than the primary. Step-down transformers reduce the voltage by having fewer turns on the secondary coil
Why will transformers only work with alternating current
Transformers only work with alternating current — the changing voltage means the flux linkage in the iron core is constantly changing, which is what causes a voltage to be induced in the secondary coil. If you used direct current (d.c.), not much would happen. Real-life transformers aren't 100% efficient — some power is always lost.
What does the magnetic field lines around a current carrying wire look like
When current is flowing in a wire, a magnetic field is induced around it. The field lines are concentric circles circled around the center of the wire The direction of the field lines can be found using the right hand rule
How can you find the magnetic flux if the magnetic flux isn't perpendicular to the area
When the magnetic flux isn't perpendicular to the area, you need to use trigonometry to resolve the magnetic field vector into components that are parallel and perpendicular to the area. For a coil of wire with N loops, when B is not perpendicular to the plane of the loop, you can find the magnetic flux using this equation: Nɸ = BAN cos θ - where θ is the ANGLE BETWEEN the FIELD and the NORMAL to the plane of the loop - B is the magnetic flux density, A is the area and N is the number of loops
What is the force on the wire in a current carrying magnetic field when the angle, θ, is changed from 0 to 90 degrees?
When θ = 0 F = BIl sin0 = BIl x 0 = 0 N When θ = 30 F = BIl sin30 = BIl x 0.5 = 0.5BIl When θ = 90 F = BIl sin90 = BIl x 1 = BIl When θ = 90, i.e. the wire is perpendicular to the magnetic field and there is the maximum force. When θ = 0, the wire is parallel to the magnetic field and there is no force
Example A current-carrying wire of length 125 mm runs at 90° to a uniform magnetic field with a flux density of 18 mT. Given that the wire experiences a force of 0.013 N, calculate the current in the wire.
l = 125 x 10^-3 B = 18 x 10^-3 F = BIl I = F/Bl = 0.013/(18 x 10^-3)(125 x 10^-3) I = 5.777 A I = 5.8 A
How can an emf be induced in a solenoid
An e.m.f. is induced whenever the magnetic fields/magnetic flux that passes through a conductor changes. You can induce an e.m.f. in a solenoid by: - moving the magnet towards or away from the coil - moving the coil towards or away form the magnet If the coil is part of a complete circuit, an induced current will flow through it.
What is an alternator and how does it work basically
An alternator is a generator of alternating current 1) Generators, or dynamos, convert kinetic energy into electrical energy — they induce an electric current by rotating a coil in a magnetic field. 2) The diagram shows a simple alternator — a generator of a.c. It has slip rings and brushes to connect the coil to an external circuit. 3) The output voltage and current change direction with every half rotation of the coil, producing an alternating current.
What is magnetic flux and how can it be calculated
Magnetic flux density is the number of field lines per unit area (Wb/m^2), so magnetic flux is the total number of field lines (in webers, Wb) ɸ = BA ɸ is magnetic flux in Wb B is magnetic flux density (T = Wb/m^2) A is area in m^2
What graphs can be derived/drawn from Faraday's law equation
You can plot a graph of flux linkage, Nɸ, against time, t. This is a straight line graph through the origin. The gradient of this graph gives you the emf You can also plot a graph of emf, ε, against time, t. This is a straight line graph in the form y = k where k is a constant. The area under the graph gives the CHANGE IN flux linkage
How can you use Flemming's left hand rule to find the direction of an induced current
• Lenz's law states that the induced current will produce a force that opposes the direction of motion of the conductor - in other words resistance • Using Fleming's left-hand rule, point your thumb in the direction of the force of resistance — which is in the opposite direction to the motion of the conductor. • Point your first finger in the direction of the field. Your second finger will now give you the direction of the induced e.m.f. • If the conductor is connected as part of a circuit, a current will be induced in the same direction as the induced e.m.f.
