Ampere's Law (Solenoid & Toroid) – AP Physics C E&M | ShowMeClass

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Ampère's Law

AP Physics C E&M · Unit 5: Magnetism

Learning Objectives

Apply Ampère's law: ∮ B·dl = μ0 I_enc

Calculate B inside/outside a solenoid

Calculate B inside a toroid

Choose appropriate Amperian loops

Key Equations

Key Insights

Solenoid: B uniform inside, ~0 outside. B = μ0nI

Toroid: B = μ0NI/(2πr) inside ring, 0 outside

Thick wire: B rises linearly inside, falls as 1/r outside

Colors

Current / coils

B-field

Amperian loop

Probe point

Ampère's LawSolenoidToroid

|B| =-

I_enc =-

probe =-

|B| vs DISTANCE

Geometry

Current I (A) 5

Turns N 200

Length L (cm) 20

Inner Radius a (cm) 8

Outer Radius b (cm) 12

Wire Radius R (cm) 3

Probe distance (cm) 5

Display

Ampère's Law Analysis

Quick Quiz▼

1. B inside an ideal solenoid with n turns/m is:

mu0*n*I mu0*N*I/(2*pi*r) mu0*I/(2*pi*r) 0

2. B outside an ideal solenoid is:

mu0*n*I Approximately zero mu0*I/(2*pi*r) Infinite

3. Inside a toroid, B depends on:

Distance r from center Only N and I Only the outer radius Length of toroid