20. Magnetic fields

A magnetic field is a region where magnetic poles, moving charges or current-carrying conductors experience magnetic force.

Separate field source from test object: stationary charges do not feel magnetic force, while currents and moving charges can.

A current in a wire creates a field around the wire; a nearby compass aligns with the local field direction.

A magnetic field is not simply another name for electric field, and it does not act on every charge regardless of motion.

Magnetic field lines show the direction a north test pole would move and use spacing to represent relative field strength.

Lines form continuous loops, are denser where the field is stronger and do not cross at a point.

Around a long straight current-carrying wire, field lines are concentric circles whose direction follows the right-hand grip rule.

Magnetic field lines do not begin and end like isolated electric lines; they continue through the magnet.

A current-carrying conductor experiences magnetic force when its current has a component perpendicular to an external magnetic field.

Reverse current or field direction to reverse force. Parallel current and field produce no force in the ideal straight-wire model.

A wire between magnet poles deflects when current flows, forming the basis of a simple motor.

The force is not caused by current alone; it requires interaction with an external magnetic field.

For wire length L carrying current I in field B at angle θ, force magnitude is F=BIL sinθ.

Use θ between current direction and field, and apply Fleming’s left-hand rule or a vector cross product for direction.

A 0.20 m wire carrying 3 A perpendicular to 0.50 T field experiences 0.30 N.

Using BIL without checking angle overestimates force when the conductor is not perpendicular.

For a wire perpendicular to a field, B=F/(IL), measured in tesla, so 1 T=1 N A⁻¹ m⁻¹.

The definition assumes the conductor is perpendicular; otherwise divide by IL sinθ or resolve the perpendicular component.

A 0.40 N force on a 0.20 m wire carrying 2.0 A gives B=1.0 T when perpendicular.

Tesla is not force per charge; that relates to electric field, while B describes magnetic force on current or moving charge.

For charge q moving at speed v through field B, magnetic force magnitude is F=Bqv sinθ and direction is perpendicular to v and B.

Use the right-hand rule for positive charges and reverse the direction for negative charges. A stationary charge feels no magnetic force.

A charged particle entering perpendicular to a uniform field follows circular motion because the force continually turns its velocity.

Magnetic force does no work on an isolated moving charge because it is perpendicular to velocity, so speed stays constant.

A charge Q moving at speed v through magnetic field B feels force magnitude F=BQv sinθ, where θ is the angle between velocity and field.

Use the right-hand rule for a positive charge and reverse direction for a negative charge. The force is zero for parallel motion.

A charge entering perpendicular to B experiences maximum force and follows a circular path if no electric field acts.

Magnetic force depends on velocity direction, not simply speed; a stationary charge feels no magnetic force.

Moving charge carriers are deflected sideways by a magnetic field, building a transverse Hall voltage until electric and magnetic forces balance.

The sign and size depend on carrier type, current, field, thickness and orientation. At balance qE_H=qvB.

Reversing the magnetic field reverses Hall voltage, while increasing current increases the voltage for a fixed sample.

Hall voltage is not the ordinary voltage drop along the conductor; it is transverse to current.

A Hall probe uses a known current and Hall coefficient so measured transverse voltage can be converted to magnetic flux density.

Keep probe face orientation, current and calibration fixed; reverse or zero the probe to identify offsets and field direction.

A probe calibrated at 20 mV T⁻¹ giving 6 mV indicates B=0.30 T under the stated operating current.

A Hall probe does not directly measure force or electric potential of the source; it infers B from carrier deflection.

With velocity perpendicular to a uniform B, magnetic force provides centripetal force, so the particle follows circular motion with r=mv/(BQ).

Speed remains constant because magnetic force is perpendicular to velocity; reverse charge or field reverses curvature.

A faster particle follows a larger-radius path in the same field, while a more highly charged particle curves more tightly.

Magnetic field changes direction of velocity, not speed, and the path is helical if velocity has a component parallel to B.

In a velocity selector, electric and magnetic forces oppose. Particles pass undeflected when qE=qvB, so v=E/B.

This condition assumes perpendicular, uniform fields and the correct orientation; faster or slower particles deflect.

E=2.0×10⁴ N C⁻¹ and B=0.50 T select v=4.0×10⁴ m s⁻¹.

The selector does not select charge sign or mass directly; it selects speed, with curvature after the selector used for further analysis.

A long straight current gives concentric circular fields; a flat current sheet gives parallel fields; a long solenoid gives an approximately uniform internal field.

Use the right-hand grip rule and distinguish ideal interior uniformity from edge fringing. Field strength depends on current and geometry.

Reversing current in a solenoid reverses its north and south poles and the internal field direction.

Field lines around a straight wire are not parallel, and a real solenoid’s field is not perfectly uniform outside its ends.

For a long solenoid, field strength is approximately proportional to current and turns per unit length; a high-permeability core can increase it further.

Use the right-hand grip rule for polarity and distinguish ideal uniform interior field from fringing at the ends.

Increasing turns per metre or current strengthens the field, while reversing current reverses the poles.

A solenoid is not a permanent magnet by default; its field depends on current and core conditions.

Each current creates a magnetic field that acts on the other conductor, producing attraction for currents in the same direction and repulsion for opposite directions.

Use the field of one wire and F=BIL on the other; the force per length falls as separation increases.

Two long parallel wires carrying equal currents in the same direction pull toward each other.

The force is not an action of one current on itself; it is an interaction between the fields and the other conductor’s current.

Magnetic flux through a surface is Φ=BA cosθ, where θ is the angle between field and the surface normal; units are webers.

Use the component of B perpendicular to the area and state the surface orientation.

A 0.20 T field through 0.50 m² perpendicular surface gives 0.10 Wb.

Flux is not simply B times any projected length, and it is zero when the field lies entirely in the plane of the surface.

When a uniform field is perpendicular to area A, magnetic flux simplifies to Φ=BA.

If the field is tilted, include cosθ; if the area or field varies, integrate or use a suitable average.

Doubling loop area doubles flux at fixed B, while rotating it edge-on reduces perpendicular flux toward zero.

The area is the surface enclosed by the loop, not the wire length.

Flux linkage is NΦ for a coil of N turns when each turn links the same flux; it measures the total linked flux that can induce emf.

Changing turns, field, area or orientation can change linkage. Distinguish flux through one turn from linkage of the whole coil.

A 100-turn coil with 2 mWb per turn has flux linkage 0.20 Wb-turn.

NΦ is not magnetic flux in one turn and does not have the same physical unit interpretation as Φ alone.

When magnetic flux linkage changes, an emf is induced; the induced effect opposes the change according to Lenz’s law.

Change field, area, orientation or motion to change linkage. A complete conducting path is needed for induced current, but emf can exist with an open circuit.

Moving a magnet into a coil gives a transient current whose direction reverses when the magnet is withdrawn.

A static magnetic field alone does not induce emf; it must produce changing flux linkage through the circuit.

Faraday’s law states that induced emf magnitude is the rate of change of flux linkage; Lenz’s law says the induced effect opposes the change causing it.

Change field, area, orientation, turns or motion to change linkage, and use the negative sign as a direction rule.

Moving a magnet faster into a coil produces a larger transient emf; withdrawing it reverses the induced current.

The negative sign does not mean emf is negative in every measurement; it encodes opposition to the change.