The Physics
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# Ampère's Law

## Practice

### practice problem 1

Use the Biot-Savart law to determine the magnetic field strength…
1. a distance r away from an infinitely long current carrying wire
2. a distance x away from a loop of current with radius a (on the axis of the loop).
3. anywhere inside a solenoid with n turns per unit length

#### solution

These problems were solved in the discussion page of this topic. Here are the results once more without any detail.

1. A distance r away from an infinitely long current carrying wire B = μ0I 2πr
2. A distance x away from a loop of current with radius a (on the axis of the loop)

Magnify

 B = μ0I a2 2 (x2 + a2)3/2
3. Anywhere inside a solenoid with n turns per unit length

[solenoid pic goes here]

B = μ0nI

### practice problem 2

Use Ampére's law to determine the magnetic field strength…
1. a distance r away from an infinitely long current carrying wire
2. anywhere on either side of an infinite, flat sheet with a surface current density σ
3. inside a solenoid with n turns per unit length
4. inside a toroid (a toroidal solenoid) with a total of N turns
5. inside a wire of radius R at any distance r from its axis

#### solution

These problems were solved in the discussion page of this section. No need to write them out in full again. Here's a summary of the results.

1. a distance r away from an infinitely long current carrying wire

[straight wire with amperean path goes here]

 B = μ0I 2πr
2. anywhere on either side of an infinite, flat sheet with a surface current density σ

[infinite sheet with amperean path goes here]

 B = μ0σ 2
3. anywhere inside a solenoid with n turns per unit length

[solenoid with amperean path goes here]

B = μ0nI

4. anywhere inside a toroid (a toroidal solenoid) with a total of N turns

[toroid with amperean path goes here]

 B = μ0NI 2πr
5. inside a wire of radius R at any distance r from its axis

[amperean path inside a wire goes here]

Inside a wire with total current I.

 B = μ0Ir 2πR2

Inside a wire with uniform current density ρ.

 B = μ0ρr 2

Write something.