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Magnetic Fields
A magnetic field is a region of space in which a magnetic pole will experience a force A magnetic field is created around a current-carrying wire due to the movement of electrons Magnetic Flux Density The strength of a magnetic field can be described by the density of its flux lines Magnetic flux density (or magnetic field strength), B, is defined as the force per unit length per unit current of the wire when the wire is perpendicular to the magnetic field One tesla is defined as the magnetic flux density that produces a force of 1N on a 1m wire carrying a current of 1A perpendicular to the magnetic field The higher the flux density, the stronger the magnetic fields (regions where flux lines are closer together) The lower the flux density, the weaker the magnetic field (regions where flux lines are further apart)
Magnetic Force on a Current-Carrying
Conductor
A current-carrying conductor produces its own magnetic field When interacting with an external magnetic field, it will experience a force The force F on a conductor carrying current I at an angle θ to a magnetic field with flux density B is defined by the equation F = BIL sinθ F = force on current-carrying conductor in a B field (N) B = magnetic flux density of applied B field (T)
I = current in the conductor (A) L = length of the conductor (m) θ = angle between the conductor and applied B field Equation shows that the force on the conductor can be increased by Increasing strength of magnetic field Increasing current flowing through conductor Increasing length of the conductor in the field A current-carrying conductor will experience the maximum magnetic force if the current through it is perpendicular to the direction of the magnetic field lines It experiences no force if it is parallel to magnetic field lines Maximum force occurs when sinθ = 1 θ = 90° and conductor is perpendicular to the B field Equation for magnetic force becomes: F = BIL Minimum force occurs when sinθ = 0° This means θ = 0° and the conductor is parallel to the B field Observing the Force on a Current-Carrying Conductor Force due to magnetic field can be observed by placing copper rod in uniform magnetic field and then connecting rod to a circuit When a current is passed through the rod, it experiences a force which causes it to accelerate in the direction of the force
perpendicular to the particle’s velocity v and directed towards the centre of the path, resulting in circular motion Magnetic force F provides centripetal force on particle F = mv^2 / r mv^2 / r = BQv r = mv / BQ r = radius of path (m) m = mass of particle (kg) v = linear velocity of particle (ms-1) B = magnetic field strength (T) Q = charge of the particle (C) Equation shows: Faster moving particles move in larger circles (larger r): r ∝ v Greater mass move in larger circles: r ∝ m Particles with greater charge move in smaller circles: r ∝ 1/ q Particles moving in a stronger magnetic field B move in smaller circles: r ∝ 1 / B Cyclotrons (type of particle accelerator) Makes use of the circular trajectory of charged particles in a magnetic field to create a spiral path Accelerates charged particles such as protons to very high speeds Cyclotron is made up of two semicircular electrodes (Dees) with a uniform magnetic field applied perpendicular to the plane of the electrodes and an alternating pd applied between the electrodes. Each Dee is a metal electrode with opposite charges that creates an electric field in the gap between the two Dees which accelerates the particles
Magnetic field causes particle to move in a circular motion which allows it to gain speed. As they speed up the radius of their motion increases until it exits
Magnetic Flux
Electromagnetic induction is the process of inducing an emf in a conductor when there is relative movement between a charge and a magnetic field Can be observed using a magnet and a coil or a solenoid This happens when a conductor cuts through magnetic field lines Amount of emf induced is determined by the magnetic flux Amount of magnetic flux varies as the coil rotates within the field Flux is the total magnetic field that passes through a given area It is a maximum when the magnetic field lines are perpendicular to the plane of the area It is 0 when the magnetic field lines are parallel to the plane of the area Magnetic flux is defined as the product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density Φ = BA Φ = magnetic flux (Wb) B = magnetic flux density (T) A = cross-sectional area (m^2 )
Magnetic Flux Linkage
More coils in a wire mean a larger emf is induced Magnetic flux linkage is a quantity commonly used for solenoids which are made of N turns of wire
Magnetic field lines may not be completely perpendicular to the plane of the area that they pass through Therefore, component of the flux density which is perpendicular is equal to θN = BAN cosθ N = number of turns of the coil
Principles of Electromagnetic Induction
Electromagnetic induction occurs when an emf is induced when a conductor moves through a magnetic field When the conductor cuts through the magnetic field lines: This causes a change in magnetic flux (ΔΦ) Which causes work to be done This work is then transformed into electrical energy Electromagnetic induction is defined as the process by which an emf is induced in a circuit due to changes in magnetic flux This can occur when: A conductor cuts through a magnetic field The direction of a magnetic field through a coil changes
Faraday’s & Lenz’s Laws
Faraday’s Law: Induced EMF is directly proportional to the rate of change of flux linkage and rate of cutting of flux Lenz’s Law: Direction of the induced EMF is always opposite to the change producing it ε = – N x ΔΦ / Δt Equation shows:
When a bar magnet goes through a coil, an emf is induced within the coil due to a change in magnetic flux Current is also induced which means the coil now has its own magnetic field Coil’s magnetic field acts in the opposite direction to the magnetic field of the bar magnet (shown by minus sign)
Applications of EM Induction
Moving conductors in a Magnetic Field Similar to a coil or a solenoid, a straight conducting rod moving through a magnetic field will also have an emf induced in it The maximum emf is induced when the conductor moves perpendicular to the magnetic field lines where it cuts through the greatest amount of magnetic flux The conducting rod has a length L and moves through a uniform magnetic field with flux density B at a constant velocity v s = vΔt s = distance travelled v = velocity Δt = time interval Area A of the magnetic flux that it cuts through is: A = LvΔt Total flux the conductor cuts through is: ΔΦ = BA = BLvΔt Faraday’s Law gives emf induced: ε =N x ΔΦ / Δt Substituting change in magnetic flux ΔΦ into the emf equation: ε = BLvΔt / Δt
t = time Equation shows that emf varies sinusoidally (having a magnitude that varies in the form of a sine wave) and is 90° out of phase with the flux linkage
Alternating Current & Voltage
An alternating current is defined as a current which periodically varies between a positive to a negative value with time This means direction of an a.c. varies every half cycle Variation of current or pd with time can be described as a sine curve o Electrons in a wire carrying a.c. move back and forth with SHM Relationship between time period and frequency for a.c. is: o T = 1 / f Peak current (I 0 ) or peak voltage (V 0 ) is defined as the maximum value of the a.c. or voltage Peak current or voltage can be determined from the amplitude of a current-time or voltage-time graph Peak-to-peak current or voltage is the distance between a positive and consecutive negative peak meaning peak voltage V0 = peak- to-peak voltage / 2 Root Mean Square Current & Voltage Root mean square (rms) values of current or voltage are a useful way of comparing a.c. current or voltage to its equivalent direct current (d.c) or voltage Rms values represent direct current or voltage values that will produce the same heating effect or power dissipation as the alternating current or voltage Rms value of an alternating current is defined as the square root of the mean of the squares of all the values of the current in one cycle The rms current Irms is defined by the equation o Irms = I 0 / √
I 0 = peak current Rms value of an alternating voltage is defined as the square root of the mean of the squares of all the values of the voltage in one cycle The rms voltage Vrms is defined by the equation: o Vrms = V 0 / √ V 0 = peak voltage The rms value is defined as the steady direct current or voltage that delivers the same average power in a resistor as the alternating current or voltage Average power of a supply is the product of the rms current and voltage o Average power = Irms x Vrms
Operation of an Oscilloscope
A Cathode Ray Oscilloscope is a laboratory instrument used to display, measure and analyse waveforms of electrical circuits o It can therefore be used as an a.c and d.c voltmeter An a.c voltage on an oscilloscope is represented as a transverse wave o Can determine its frequency, time period and peak voltage A d.c. voltage on an oscilloscope is represented as a horizontal line at the relevant voltage X axis is the time and y axis is the voltage Period of the wave can be determined from the time-base o This is how many seconds each division represents measured commonly in s div-1^ or s cm- Frequency is determined through o f = 1 / T
o Step up transformer (increases the voltage of the power source) where Ns > Np o Step down transformer (decreases the voltage of the power source) where Np > Ns
Transformer Efficiency
Power in = power out o Ip Vp = Is Vs Ip = current in primary coil Vp = voltage in primary coil Is = output current from secondary coil Vs = output voltage from secondary coil Transformer efficiency = Is Vs / Ip Vp Eddy Currents Eddy currents are a key source of energy loss in a transformer which makes them unlikely to be 100% efficient They arise from: o Changing magnetic field (and flux) from the a.c. or voltage o Which creates a changing magnetic field in the core that acts against the field that induced them o An emf is therefore induced o A current flows, as core is made from a conducting material Current also dissipates energy by generating heat in the wires Eddy currents are reduced by: o Laminating the iron core with layers of insulation o Having a core made from a high resistivity metal The laminations are insulated from each other, so the current doesn’t flow between them Eddy current: as the primary coils magnetic field induces EMF in the secondary coil, it also induces EMF and mini currents in the iron core (eddy currents)
FE = FB
FE = EQ
FB = BQv EQ = BQv E = Bv E = Vh / d Vh / d = Bv Vh = Bvd
