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Opus in profectus

Ampère's Law

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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
    r
  2. a distance x away from a loop of current with radius a (on the axis of the loop)

    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
    r
  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
    r
  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
    R2

    Inside a wire with uniform current density ρ.

    B =  µ0ρr
    2

practice problem 3

Write something.

solution

Answer it.

practice problem 4

Write something completely different.

solution

Answer it.