Physics › Magnetic fields › Magnetic flux density and the force on a wire
Magnetic flux density and the force on a wire
The third field breaks the family pattern: its force acts on moving charge, not on a standing property, and it pushes sideways, at right angles to both the current and the field. One formula, one left hand, and a top-pan balance to measure it all.
Builds on The field concept and Current, charge and the direction problem.
IN THIS TOPIC
- Use F = BIl for a wire perpendicular to the field, and Fleming's left hand rule for directions.
- Define magnetic flux density and the tesla.
- Describe the required-practical measurement of the force with a top-pan balance.
WHAT YOU PROBABLY THINK
Fields always push along their field lines.
A sideways force
Gravitational fields pull masses along the field lines; electric fields push charges along them. The magnetic field breaks the pattern twice over: it acts only on moving charge, a current, and its force points at right angles to both the current and the field. For a straight wire of length l carrying current I across a field of flux density B, the magnitude is
valid when field and current are perpendicular. The direction comes from Fleming's left hand rule: First finger along the Field, seCond finger along the Current, and the thuMb gives the Motion, the force, with all three held at right angles. Diagrams handle the third dimension with the standard symbols, a circled cross for a field into the page and a circled dot for one coming out.
The right angle is not decoration. A wire lying along the field feels no force whatsoever, and at intermediate angles only the perpendicular arrangement's share survives. The lie above dies here: this field never pushes along its own lines.
Flux density, and the tesla
Rearranging the force law defines the field's strength. The magnetic flux density B is the force per unit current per unit length of perpendicular wire, B = F/Il, and its unit, the tesla, follows: one tesla is the flux density that puts one newton on each metre of wire carrying one amp at right angles to the field. A tesla is a substantial field; laboratory magnets sit in the tens of milliteslas, and the Earth's field is a few hundredths of one.
Required practical 10: weighing a force
The tenth required practical measures the force with nothing more exotic than a top-pan balance. A magnet sits on the balance and a stiff wire is clamped, separately, between its poles. Switch the current on and the field pushes the wire, say upward; by Newton's third law the wire pushes the magnet downward with an exactly equal force, and the balance reading rises by F/g. Varying the current, the wire length in the field, and the flux density then tests each proportionality in F = BIl in turn, converting grams of reading change back to newtons each time.
THE EXAM BIT
- F = BIl holds for the perpendicular arrangement; say so when you quote it, and give zero force without calculation for a wire along the field.
- Fleming's left hand needs the current direction as conventional current. Electron flow questions are the planted trap: reverse it first.
- Define the tesla operationally: one newton per amp per metre of perpendicular wire. The definition is the rearranged force equation in words.
- Into-page and out-of-page symbols are examinable vocabulary: circled cross in, circled dot out. Read them before reasoning.
- In the balance practical, the mark scheme wants Newton's third law named: the force on the magnet is the equal and opposite partner of the force on the wire, and the reading change is F/g.
CHECK YOURSELF
A wire carries 3.0 A at right angles across a field of 0.20 T, with 5.0 cm of the wire in the field. Find the force, and the change in reading of a balance supporting the magnet, in grams.
Show a hint
F = BIl in base units, then grams via g.
Show the answer
F = BIl = 0.20 × 3.0 × 0.050 = 0.030 N.
The magnet feels the equal and opposite partner force, so the reading changes by F/g = 0.030 / 9.81 = 3.1 × 10−3 kg, about 3.1 g.
Whether the reading rises or falls depends on the current's direction; reversing it flips the change, which is itself a check the effect is real.
The magnetic force acts on current, at right angles to everything.
One tesla: one newton per amp per metre of crossing wire.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.