B = μ₀/(2π)(I/r) gives the magnitude of the magnetic field at a perpendicular distance r from a long, straight wire carrying current I, where μ₀ is the permeability of free space. The field is proportional to current and falls off as 1/r, wrapping in circles around the wire.
This is the equation for the magnetic field created by a long, straight, current-carrying wire. Plug in the current I and the perpendicular distance r from the wire's central axis, and you get the field strength B at that point. The constant μ₀ is the permeability of free space, which sets how strong a magnetic field a given current produces.
The equation tells you two relationships the AP exam loves to test. First, B is directly proportional to I, so doubling the current doubles the field. Second, B is inversely proportional to r (note: 1/r, not 1/r²), so doubling your distance from the wire halves the field. The direction isn't in the formula at all. The field vectors are tangent to concentric circles centered on the wire, with zero component toward, away from, or parallel to the wire. You find which way the circles point with the right-hand rule: thumb along the current, fingers curl in the direction of B.
This equation is the centerpiece of Topic 12.3 (Magnetism and Current-Carrying Wires) in Unit 12: Magnetism and Electromagnetism. It directly supports learning objective 12.3.A, which asks you to describe the magnetic field produced by a current-carrying wire, both its magnitude (this formula) and its circular geometry. It's also the bridge to 12.3.B, because once one wire creates a field, a second wire sitting in that field feels a force given by F_B = IℓB sin θ. That two-wire setup, where you calculate B from one wire and then the force on the other, is one of the most common ways Unit 12 chains two equations into a single problem. Conceptually, this is also where electricity and magnetism fuse. Moving charge doesn't just respond to magnetic fields; it creates them.
Keep studying AP® Physics 2 Unit 12
F_B = IℓB sin θ (Unit 12)
These two equations are a matched pair. B = μ₀/(2π)(I/r) tells you the field a wire makes, and F_B = IℓB sin θ tells you the force a wire feels when sitting in a field. Classic two-wire problems use both: wire 1's current creates B at wire 2's location, then that B exerts a force on wire 2. Parallel currents attract, antiparallel currents repel.
Permeability of free space (Unit 12)
μ₀ is the constant that converts current into magnetic field strength. It plays the same structural role for magnetism that the Coulomb constant plays for electric fields. It's on the AP formula sheet, so you don't memorize its value, but you should recognize it as the magnetic constant of the vacuum.
Right-hand rule for field direction (Unit 12)
The equation only gives magnitude. Direction comes from curling your right hand: point your thumb along the current and your fingers wrap in the direction of the circular field lines. AP questions frequently ask for the field direction at a point above, below, or beside a wire, and the formula alone can't answer that.
Electric field of a point charge (Unit 11)
Comparing the two is a great mental check. A point charge's electric field drops off as 1/r², but a long straight wire's magnetic field drops off as 1/r. Mixing up these falloff rates is a common MCQ trap, so remember the wire's field weakens more slowly with distance than a point charge's field does.
Expect this equation in multiple-choice questions that test proportional reasoning rather than raw computation. A typical stem says the current doubles and the distance triples, then asks for the new field as a multiple of the original (answer: 2/3 B). Another favorite asks you to rank field strengths at points around one or two wires, or to find where the fields of two parallel wires cancel. On free-response questions, this formula usually appears as step one of a chain. You calculate B from one wire, then feed it into F_B = IℓB sin θ to find the force on a nearby wire or moving charge, and justify direction with the right-hand rule. No released FRQ hinges on this equation alone, but describing a wire's field, magnitude AND circular direction, is exactly what LO 12.3.A asks you to do, and qualitative justification questions reward you for stating the 1/r dependence explicitly.
B = μ₀/(2π)(I/r) describes the field a wire CREATES; F_B = IℓB sin θ describes the force a wire FEELS from an external field. The giveaway is the question's verb. 'What field does the wire produce at point P?' means use the first equation. 'What force acts on the wire?' means use the second. In two-wire problems you use both, in that order, and the I in each equation refers to a different wire.
B = μ₀/(2π)(I/r) gives the magnetic field magnitude at perpendicular distance r from a long, straight wire carrying current I.
The field is directly proportional to the current and inversely proportional to distance, so it falls off as 1/r, not 1/r².
The field lines form concentric circles around the wire, with no component pointing toward, away from, or parallel to the wire.
Direction comes from the right-hand rule: thumb points along the current, fingers curl in the direction of the field.
In two-wire problems, use this equation to find the field from one wire, then F_B = IℓB sin θ to find the force on the other.
μ₀, the permeability of free space, is a constant on the formula sheet, so focus your energy on the I and r relationships.
It's the equation for the magnetic field strength at a perpendicular distance r from a long, straight wire carrying current I. It's covered in Topic 12.3 of Unit 12 and supports learning objective 12.3.A.
No. The field from a long straight wire falls off as 1/r, not 1/r². Double your distance from the wire and the field halves; quadruple the distance and you get one quarter of the field. The inverse-square falloff belongs to point charges, not long wires.
The first calculates the field a current-carrying wire produces in the space around it. The second calculates the force a wire experiences when it sits in someone else's magnetic field. AP problems often chain them: find B from wire 1, then plug it into the force equation for wire 2.
Use the right-hand rule. Point your right thumb in the direction of the current and your fingers curl in the direction of the field, which wraps around the wire in concentric circles. The equation itself only gives magnitude.
No, it's on the official equation sheet, along with the value of μ₀. What you do need is to recognize when to use it, reason about proportionality (like what happens to B when I doubles or r triples), and pair it with the right-hand rule for direction.
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