Physics II - B14

TABLE OF CONTENTS

• Magnetic Force Between Two Parallel Conductors
• Magnetic Field for a Long, Straight Conductor
• Magnetic Field for a Circular Current Loop
• Magnetic Field Lines for a Loop
• Ampere’s Law
• Long Wire with Finite Thickness
• Magnetic Field of a Toroid
• Magnetic Field of a Solenoid

Magnetic Force Between Two Parallel Conductors

$$\vec F_1 = I_1\vec l \times \vec B_2$$ $$\to F_1 = I_1lB$$ $$B_2 = \frac{\mu_0I_2}{2\pi a}$$ $$\frac{F_1}{l} = \frac{\mu_0I_1I_2}{2\pi a} = \frac {2\times10^{-7} (N)}{1(m)} = \frac{\mu_0 (1A)^2}{2\pi (1m)}$$

$\Rightarrow$ the definition of Ampere

Parallel conductors carrying currents in the same direction attract each other, and parallel conductors carrying currents in opposite directions repel each other.

Magnetic Field for a Long, Straight Conductor

Magnetic Field for a Circular Current Loop

Magnetic Field Lines for a Loop

Ampere’s Law

Long Wire with Finite Thickness

Magnetic Field of a Toroid

Magnetic Field of a Solenoid

• The magnetic field lines resemble that of a magnet.

• Uniform field: parallel and equally spaced

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