Magnetic Fields Flashcards
(29 cards)
What happens when current passes through a wire?
a magnetic field is induced - this is true for any long, straight current-carrying conductor. This field lines of the induced magnetic field form concentric rings around the wire.
The magnetic flux density (B) of a magnetic field
is a measure of the strength of the field, and it is measured in the unit Tesla. One Tesla is defined as a force of 1 N on 1 metre of wire carrying 1 A of current perpendicular to a magnetic field.
What happens when a current-carrying wire is placed in a magnetic field?
a force is exerted on the wire. However, if the current is parallel to the magnetic field, the force is 0 N, because no component of the field is perpendicular to the current To find the magnitude of force (F) when the wire of length l , carrying a current I, is placed into a field of flux density B, so that field is perpendicular to the current, you can use the formula:
F= BIL
F = magnetic force (Newtons, N)
B = magnetic flux density (Teslas, T)
I = current in the wire (Amperes, A)
L = length of wire in the magnetic field (metres, m)
fleming’s left hand rule
Spread out your thumb, first and second finger so that they are all perpendicular to each other, each finger represents a different quantity:
● ThuMb - represents the direction of the Motion/force
● First finger - represents the direction of the Field
● SeCond finger - represents the direction of the Conventional Current (opposite direction to electron flow)
The direction of a magnetic field on a magnet is…
is form its North pole to its South pole.
How do moving charges act in a magnetic field?
A force acts on charged particles moving in a magnetic field, this is why a force is exerted on a current-carrying wire, because it contains moving electrons, which are negatively charged particles. The magnitude of force (F) exerted on a particle with charge Q, moving at a velocity v, perpendicular to a field with flux density B, can be calculated using the following formula:
F = BQv
What direction is the force exerted?
The force exerted is always perpendicular to the motion of travel, which causes the charged particles to follow a circular path when in the magnetic field, because the force induced by the magnetic field acts as a centripetal force. By combining the formulas for centripetal force and magnetic force on a charged particle, you can find a formula to find the radius of the particle’s circular path:
What is an application of the circular deflection of charged particles in a magnetic field?
is a type of particle accelerator called a cyclotron
Explain how a cyclotron works?
- Structure of the Cyclotron
- It consists of two D-shaped metal electrodes called “Dees”, placed face-to-face with a small gap between them.
- A uniform magnetic field acts perpendicular to the plane of the Dees.
- A high-frequency alternating voltage is applied across the gap between the Dees. - Starting Point: Injection of Charged Particles
- Charged particles (like protons or ions) are released from the center of one Dee.
- As soon as they enter the magnetic field, they begin to move in a circular path due to the magnetic force acting perpendicular to their velocity (this is circular motion due to the Lorentz force: 𝐹=𝐵𝑞𝑣 - Constant Speed Inside Each Dee
- While the particle moves inside one of the Dees, it does not speed up, because the magnetic force only changes its direction, not its speed.
- The particle completes a half-circle within the Dee. - Acceleration Across the Gap
- As the particle exits one Dee and enters the gap, the alternating electric field across the gap is in the correct direction to accelerate it.
- The particle’s kinetic energy and speed increase. - Larger Circular Path in the Second Dee
- Because the particle is now faster, it follows a wider circular path in the second Dee - Repeated Acceleration
- When the particle reaches the gap again, the alternating voltage has reversed polarity just in time to accelerate it again.
- This process repeats every half-cycle, increasing the particle’s energy and radius of motion with each pass. - Exit of the Particle
- Eventually, the particle reaches the outer edge of the cyclotron.
- It is then directed out of the cyclotron, forming a high-energy beam.
Magnetic flux (ϕ)
is a value which describes the magnetic field or magnetic field lines passing through a given area, and it is calculated by finding the product of magnetic flux density (B) and the given area (A), when the field is perpendicular to the area
Magnetic flux (ϕ) equation
Φ=BAcosθ
Φ = magnetic flux (in webers, Wb)
B = magnetic flux density (in teslas, T)
A = area through which the field lines pass (in m²)
θ = angle between the magnetic field and the normal (perpendicular) to the surface
If the magnetic field is not perpendicular to a coil of wire, you can still find magnetic flux and magnetic flux linkage by using trigonometry to resolve the magnetic field vector into components, which are parallel and perpendicular to the coil.
Magnetic flux linkage (Nϕ)
is the magnetic flux multiplied by the number of turns N, of a coil
Electromagnetic induction
Electromagnetic induction is when a voltage (emf) is created because something is moving through a magnetic field, or the magnetic field is changing around something.
- First case: moving a conducting rod in a magnetic field
- A metal rod has free electrons (like tiny charged particles that can move).
- When the rod moves through a magnetic field, the electrons feel a force (called the Lorentz force).
- This force pushes electrons to one end of the rod.
- That creates a difference in charge between the two ends, this is an emf (voltage).
- If you connect the rod in a complete circuit, this emf causes a current to flow.
- This is a basic example of electromagnetic induction. - Second case: moving a magnet into a coil
- When a magnet is moved into or out of a coil of wire, the magnetic field through the coil changes.
- A changing magnetic field causes an emf to be induced in the coil (by Faraday’s Law).
- If the coil is part of a complete circuit, the emf makes a current flow.
There are two laws which govern the effects of electromagnetic induction:
- Faraday’s law - the magnitude of induced emf is equal to the rate of change of flux linkage
- Lenz’s law - the direction of induced current is such as to oppose the motion causing
How is Lenz law demonstrated?
- Setup and Observation
- You drop a magnet through a coil of wire and compare it to a magnet falling the same distance without a coil.
- Result: The magnet falls slower through the coil than in free fall. - As the Magnet Approaches the Coil
- The magnet’s motion changes the magnetic flux through the coil.
- According to Faraday’s Law, this change induces an EMF, which causes a current in the coil.
- Lenz’s Law states this induced current will oppose the change that created it — in this case, the motion of the magnet.
- So the coil produces a magnetic field with a like pole facing the approaching magnet’s pole → repels it, slowing it down. - When the Magnet is at the Centre of the Coil
- At the exact centre, the rate of change of magnetic flux is zero (field lines are symmetrical and not increasing or decreasing).
- Therefore, no EMF is induced → no current flows momentarily. - As the Magnet Exits the Coil
- The magnetic flux now decreases, again inducing an EMF.
- The coil creates a magnetic field with the opposite pole facing the magnet, trying to pull it back in → again opposing its motion.
- This attraction again slows the magnet down.
Faraday’s law equation
also
ε = Blv
What are the equations for electromagnetic induction in a coil rotating in a uniform magnetic field?
NΦ=BANcos(ωt)
N = number of turns in the coil
B = magnetic flux density (T)
A = area of the coil (m²)
ω = angular speed of rotation (rad/s)
t = time (s)
Φ = magnetic flux through one loop
NΦ = flux linkage, the total magnetic flux through all loops
This equation shows how the flux linkage varies with time as the coil rotates in the field.
Induced EMF (Faraday’s Law) equation
The minus sign (from Lenz’s Law) indicates that the EMF opposes the change in flux, but in many cases it’s omitted if you’re just finding the magnitude.
This shows that the EMF varies sinusoidally i.e., it’s AC (alternating current).
What happens when a coil rotates in a magnetic field?
an emf is induced. The value of induced emf can be calculated using the formula, ε = BANω sin(ωt) , as this contains a sine function, the induced emf is alternating, meaning it will change direction with time (shown by the change in sign).
oscilloscope, which shows the variation of voltage with time and time based turned off
What can you measure from an oscilloscope?
Transformers
Transformers can be used with alternating currents to change the size of their voltage. They are made up of a primary coil, which is attached to the input voltage, a secondary coil, which is connected to the output voltage and an iron core. The primary coil provides a changing magnetic field, which passes through the iron core and interacts with the secondary coil, inducing a voltage in the secondary coil.
By using Faraday’s law you can deduce that the ratio of…
the voltage in the primary coil to the secondary coil, is the same as the ratio of the number of turns on the primary coil to the secondary coil. This can be written as the equation
There are two types of transformer
● Step-up transformer - increases the input voltage by having more turns on the secondary coil than the primary
● Step-down transformer - decreases the input voltage by having less turns on the secondary coil.
