Magnetic fields Flashcards
Magnetic field
a field of force that is created by moving electric charge or permanent magnets
Direction of magnetic field lines
Always north -> south
- the field lines are stronger when the lines are closer, and weaker when the lines are further apart
Uniform magnetic field
the magnetic field strength is the same at all points
- represented by equally spaced parallel lines
Dots and crosses
Dots - the magnetic field OUT of the page
Crosses - the magnetic field INTO the page
Current-carrying conductor
- produces its own magnetic field
- experiences a force when PERPENDICULARLY interacting with an external magnetic field
Magnetic flux density
F = BILsinΘ
B = F / IL
the force acting per unit current per unit length on a wire placed at right angles to the magnetic field
SI unit: Tesla (T)
F = BILsinΘ shows that…
the greater the current or magnetic field strength, the greater the force on the conductor
When does F = BILsinΘ reach maximum force?
maximum: sinΘ = 1 / 90°
- this is when the conductor is perpendicular to the B (magnetic) field
- hence… F = BIL
minimum: sinΘ = 0 / 0°
- this is when the conductor is parallel to the B field
- hence F = 0
Flemings left hand rule
Thumb = motion / force
Pointer = magnetic field
Middle finger = current (direction of the current is the direction of conventional current flow)
Tesla
a straight current carrying conductor carrying a current of 1A normal to a magnetic field of flux density 1T with force per unit length of the conductor of 1Nm^-1
Force on a moving charge equation
F = BQvsinΘ
Q -> charge of the particle
Equivalent to the force on a wire, if the magnetic field B is perpendicular to the direction of the charge’s velocity, the equation simplifies to:
F = BQv
What does the equation F = BQv show?
If the direction of the electron changes, the magnitude of the force will change too
the force due to magnetic field is always perpendicular to the velocity of the electron
Hall voltage
The potential difference produced across an electrical conductor when an external magnetic field is applied perpendicular to the current through the conductor
Explain the hall effect
- When an external magnetic field is applied perpendicular to the direction of current through a conductor, the electrons experience a magnetic force
- This makes them drift to one side of the conductor, where they all gather and becomes more negatively charged
- This leaves the opposite side deficient of electrons, or positively charged
- There is now a potential difference across the conductor
- This is called the Hall Voltage, VH
Direction of velocity, electric force and magnetic force of an electron
Velocity = forward
Electric force = upwards from electron
Magnetic force = downwards from electron
Electric field strength of hall effect equation
E = Vh / d
Derivation of the Hall voltage (Vh) equation
- Fb = BQv and Fe = QE
- Therefore, QE = BQV
- Since E = VH/d , and cancelling the Q, hence Vh / d = Bv
- Since I = nAvq, v = I/nAq
- …therefore Vh/d = (B)(I/nAq)
- Since A (cross sectional area) is the product of the width (d) and the thickness (t), A = dt
- Vh/d = (B)(I/n (dt) q)
Vh = (B)(I/ntq)
What is a hall probe used for?
To measure the magnetic flux density between two magnets based on the Hall effect
How to use a hall probe to measure hall voltage?
- The flat surface of the probe must be directed between the magnets, perpendicular to the magnetic field lines
- The probe is connected to a voltmeter to measure hall voltage
- Hall voltage depends on the angle between the magnetic field and the plane of the prob (maximum = perpendicular, minimum = parallel)
Describe the path of a charged particle in a uniform magnetic field. Explain why.
A charged particle in uniform magnetic field which is perpendicular to its direction of motion travels in a CIRCULAR path
- This is because the magnetic force FB will always be perpendicular to its velocity v
- FB will always be directed towards the centre of the path, hence provides CENTRIPETAL FORCE
Equation of centripetal force
F = mv^2 / r
Derivation of the equation for the radius of the orbit of a charged particle in a perpendicular magnetic field
mv^2/r = BQv
r = mv / BQ
Velocity selector
A device consisting of perpendicular electric and magnetic fields where charged particles with a specific velocity can be filtered
Describe the construction of a velocity selector
- Consists of two horizontal oppositely charged plates situated in a vacuum chamber
- The plates provide a uniform electric field with strength E between them
- There is also a uniform magnetic field with flux density B applied perpendicular to the electric field
- If a beam of charged particles enter between the plates, they may all have the same charge but travel at different speeds v
What happens when Fe = Fb on the charged particles in a velocity selector?
The particles travelling at the desired speed v will travel through undeflected due to the equal and opposite electric and magnetic forces on them
Velocity v in a velocity selector equation
EQ = BQv
THEREFORE: v = E/B
What happens when a particle has a speed greater or less than v?
The particle
