Electromagnetism notes

MDCAT Physics

This chapter explains magnetic flux density, magnetic flux, forces on moving charges, motion of charged particles in magnetic fields, and electromagnetic induction. It also covers solenoids, magnetic materials, transformers, choke coils, eddy currents, tangent galvanometers, and the basic working of a CRO.

Magnetic Flux Density

Magnetic flux density is the magnetic force acting on a unit current-carrying conductor of unit length when the conductor is placed perpendicular to the magnetic field. It is represented by B.

The magnetic field is stronger where the flux lines are closer together. For a conductor carrying current I in a magnetic field, the force depends on the current, length, field strength, and angle between the conductor and the field.

Magnetic flux density is measured in tesla, T.
1 T = 1 N A-1 m-1.
For a straight conductor, F = BIL sin θ.
The force is maximum when the conductor is perpendicular to the magnetic field, so θ = 90 degrees.
The force is zero when the conductor is parallel to the magnetic field, so θ = 0 degrees.
The direction of force is given by Fleming's left-hand rule.
Magnetic flux density is also called magnetic induction in many FSc textbooks.

Magnetic Flux

Magnetic flux is the total magnetic field passing normally through a surface. It is represented by Φ. For a uniform magnetic field passing through a flat surface, the flux depends on the field strength, area, and the angle between the magnetic field and the normal, called the vector area.

The vector area is perpendicular to the surface. Therefore, the angle used in Φ = BA cos θ is the angle between B and the vector area, not necessarily the angle between B and the surface.

Magnetic flux is given by Φ = BA cos θ.
The SI unit of magnetic flux is the weber, Wb.
1 Wb = 1 T m2.
Flux is maximum when the angle between B and the vector area is 0 degrees.
At θ = 0 degrees, Φ = BA.
Flux is zero when the magnetic field is parallel to the surface, because it is then perpendicular to the vector area.
At θ = 90 degrees, Φ = 0.
Magnetic flux is a scalar quantity.

Motional Electromotive Force

When a conducting rod moves through a magnetic field, free charges in the rod experience a magnetic force. Positive and negative charges separate, producing a potential difference or motional e.m.f. across the rod.

For a rod of length l moving with speed v perpendicular to a magnetic field B, the induced e.m.f. is E = Blv. If the motion is not perpendicular, the general expression is E = Blv sin θ, where θ is the angle between the velocity and the magnetic field.

For l = 0.25 m, B = 0.25 T, and v = 0.5 m s-1, E = Blv = 0.03125 V, approximately 3.13 x 10-2 V.
Motional e.m.f. is produced because of the motion of the conductor through the magnetic field.
The induced current requires a closed conducting path. An e.m.f. can exist even when the circuit is open.
The direction of induced current can be found using Fleming's right-hand rule.
If the rod moves parallel to the magnetic field, v is parallel to B and the motional e.m.f. is zero.
The unit of e.m.f. is volt, V.

Force on a Charged Particle in a Magnetic Field

A charged particle moving in a magnetic field experiences a magnetic force. The force is perpendicular to both the velocity of the particle and the magnetic field. The magnetic field changes the direction of motion, but it does no work on the particle because the force is perpendicular to its displacement.

The force on a charge q moving with velocity v in a magnetic field B is F = qvB sin θ. The direction for a positive charge is found by the right-hand rule. The direction for a negative charge is opposite to the right-hand rule.

The force is maximum when v is perpendicular to B, at θ = 90 degrees.
The force is zero when the particle is stationary, because v = 0.
A stationary electron remains stationary in a magnetic field. A magnetic field alone cannot start its motion.
The force is also zero when a moving charged particle travels parallel to B.
If the velocity is perpendicular to B, the particle moves in a circular path.
For a circular path, qvB = mv2/r.
The radius of the circular path is r = mv/qB, using magnitudes.
A magnetic field changes the direction of velocity, not its magnitude.

Circular Motion and Helical Motion

When a charged particle enters a uniform magnetic field with velocity perpendicular to the field, the magnetic force acts as the centripetal force. The particle follows a circular path.

The angular speed and time period of this circular motion do not depend on the speed of the particle, provided the particle remains in the same magnetic field and its speed is non-relativistic.

The time period is T = 2πm/qB, using the magnitude of charge q.
The frequency is f = qB/2πm.
The angular frequency is ω = qB/m.
The radius increases when mass or speed increases.
The radius decreases when charge magnitude or magnetic flux density increases.
A particle entering at an angle to B has two velocity components: one perpendicular and one parallel to B.
The perpendicular component causes circular motion, while the parallel component remains uniform, producing a helical path.
Positive and negative charges curve in opposite directions in the same magnetic field.

Electromagnetic Induction and Lenz's Law

Electromagnetic induction is the production of e.m.f. in a circuit when the magnetic flux linked with the circuit changes. The change may result from motion of a magnet, motion of a coil, or a change in current in a nearby coil.

Faraday's law states that the induced e.m.f. is proportional to the rate of change of magnetic flux linkage. For N turns, E = -N dΦ/dt. The negative sign represents Lenz's law.

Lenz's law states that induced current flows in a direction that opposes the change producing it.
Lenz's law is consistent with the law of conservation of energy.
A faster change in flux produces a greater induced e.m.f.
An induced current is produced only when the magnetic flux linked with the circuit changes.
A stationary magnet near a stationary coil does not produce continuous induced current.
When a bar magnet enters and leaves a solenoid, the galvanometer deflection changes direction because the flux first increases and then decreases.
The deflection is zero when the magnet is outside the effective region or when the flux is not changing.
The induced e.m.f. in coil X due to current in neighbouring coil Y is proportional to the rate of change of magnetic field linked with coil X.

Solenoids and Magnetic Materials

A solenoid is a long coil of many closely wound turns. When current passes through it, a magnetic field is produced. The field inside a long solenoid is nearly uniform and strong, while the field outside is relatively weak.

The strength and nature of an electromagnet depend on the coil current, number of turns, dimensions of the solenoid, and the core material.

The magnetic field at the middle of a long solenoid is uniform and strong.
For a long air-core solenoid, B = μ0nI, where n is the number of turns per unit length.
Soft iron is used as the core of an electromagnet because it loses its magnetism quickly when current is switched off.
Steel retains magnetism and is suitable for permanent magnets.
Coercive force is the reverse magnetic field required to reduce the magnetisation of a material to zero.
A material with high coercive force is difficult to demagnetise.
Magnetic materials lose their magnetic properties when heated above their Curie temperature.
Soft iron has low coercivity and is easily magnetised and demagnetised.

Mutual Induction, Transformers and Choke Coils

Mutual induction is the production of an e.m.f. in one coil due to a change of current in a nearby coil. The changing current produces a changing magnetic field, which changes the flux linked with the second coil.

A transformer transfers electrical energy from one circuit to another by mutual induction. It works with alternating current because alternating current continuously changes the magnetic flux in the core.

A transformer has a primary coil, a secondary coil, and a laminated soft iron core.
For an ideal transformer, Vs/Vp = Ns/Np.
In a step-down transformer, Ns is less than Np and the secondary voltage is less than the primary voltage.
In a step-up transformer, Ns is greater than Np and the secondary voltage is greater than the primary voltage.
A transformer produces statically induced e.m.f. because its coils have no relative mechanical motion.
A choke coil has small resistance and large inductance.
A choke coil limits alternating current mainly through inductive reactance while using little electrical power.
A transformer cannot operate properly with steady direct current because the magnetic flux does not continuously change.

Eddy Currents and Magnetic Measuring Devices

Eddy currents are induced currents produced inside a bulk conductor when the magnetic flux through different parts of the conductor changes. They circulate in closed loops within the conductor.

Eddy currents can cause heating and energy loss, but they are also used in induction heating, electromagnetic braking, and some measuring instruments.

Eddy currents flow in closed loops inside a conductor.
Laminating an iron core reduces eddy current losses by increasing the electrical resistance of paths inside the core.
A tangent galvanometer uses the tangent law to measure current.
For a tangent galvanometer, I is proportional to tan θ when the magnetic field of the coil is compared with the horizontal component of Earth's magnetic field.
For coils of the same radius connected in series, the same current passes through both coils.
For such coils, N is proportional to tan θ.
For deflections of 60 degrees and 45 degrees, the ratio of turns is tan 60 degrees : tan 45 degrees = √3 : 1.
The induced effects of changing flux are explained by Faraday's law and Lenz's law.

Cathode Ray Oscilloscope

A CRO displays electrical signals on a fluorescent screen. It produces a narrow beam of electrons and controls the beam using electric fields between pairs of parallel plates.

The electron beam is deflected by a uniform electric field between two sets of parallel plates. One set gives vertical deflection and the other gives horizontal deflection.

The electron gun produces and accelerates the electron beam.
The control grid controls the brightness of the spot on the screen.
The anodes focus and accelerate the electron beam.
The vertical plates provide deflection proportional to the input voltage.
The horizontal plates usually provide a time-base voltage for observing variation with time.
The fluorescent screen produces a visible bright spot when struck by electrons.
CRO deflection is electrostatic, not magnetic, in the standard FSc instrument.

Key terms

Magnetic flux density: Magnetic force per unit current and unit length when the conductor is perpendicular to the field, represented by B.
Magnetic flux: The total magnetic field passing normally through a surface, represented by Φ.
Tesla: The SI unit of magnetic flux density, where 1 T = 1 N A-1 m-1.
Weber: The SI unit of magnetic flux, where 1 Wb = 1 T m2.
Vector area: A vector perpendicular to a surface whose magnitude is equal to the area of that surface.
Motional e.m.f.: The e.m.f. produced when a conductor moves through a magnetic field.
Magnetic force: The force exerted by a magnetic field on a moving charged particle or current-carrying conductor.
Cyclotron radius: The radius of the circular path of a charged particle moving perpendicular to a uniform magnetic field.
Electromagnetic induction: The production of e.m.f. due to a change in magnetic flux linked with a circuit.
Lenz's law: The induced current opposes the change in magnetic flux that produces it.
Mutual induction: The production of e.m.f. in one coil due to a changing current in a nearby coil.
Solenoid: A long coil of many closely wound turns that produces a magnetic field when current passes through it.
Coercive force: The reverse magnetic field required to remove magnetisation from a magnetic material.
Eddy currents: Induced currents that flow in closed loops inside a bulk conductor.
Choke coil: A coil with small resistance and large inductance used to limit alternating current.
Transformer: A device that transfers electrical energy between coils through mutual induction.
Control grid: The CRO electrode that controls the brightness of the electron spot.

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Physics shortcuts

Comparing distance and displacement

Distance equals the magnitude of displacement only when the particle travels along a straight path without reversing direction.

Check whether the path is straight and one-directional.
If yes, distance = |displacement|.
Example: A particle moves 5 m east in a straight line. Distance = 5 m and displacement magnitude = 5 m.

This shortcut does not apply to a curved path or to motion involving a change of direction.

Projectile range and components

For a projectile launched and landing at the same level, use R = u² sin 2θ/g. Resolve the initial velocity into horizontal and vertical components when needed.

Write ux = u cos θ and uy = u sin θ.
For the same launch and landing level, R = u² sin 2θ/g.
Example: u = 20 m/s, θ = 30°, g = 10 m/s². R = 400 sin 60°/10 = 34.6 m.

The range formula does not apply directly when the projectile lands at a different height.

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