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Ampere’s Law. Outline. Introduce Ampere’s Law as an analogy to Gauss’ Law. Define Ampere’s Law. Show how to use Ampere’s Law for cases with symmetry. Student Objectives. Recognise Ampere’s Law to be analogous to Gauss’ Law.

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Presentation Transcript
outline
Outline
  • Introduce Ampere’s Law as an analogy to Gauss’ Law.
  • Define Ampere’s Law.
  • Show how to use Ampere’s Law for cases with symmetry.
student objectives
Student Objectives
  • Recognise Ampere’s Law to be analogous to Gauss’ Law.
  • Recognise similar concepts: (1) draw an imaginary shape enclosing the current carrying conductor, (2) current enclosed.
ampere s law4
Ampere’s Law
  • Gauss’ law allowed us to find the net electric field due to any charge distribution (with little effort) by applying symmetry.
  • Similarly the net magnetic field can be found with little effort if there is symmetry using Ampere’s law.
ampere s law5
Ampere’s Law
  • Ampere’s law,
  • Where the integral is a line integral.
  • B.ds is integrated around a closed loop called an Amperian loop.
  • The current ienc is net current enclosed by the loop.
ampere s law6
Ampere’s Law
  • ie,
  • ie ienc
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Ampere’s Law
  • The figure shows the cross section of 3 arbitrary long straight wires with current as shown.
ampere s law8
Ampere’s Law
  • Two of the currents are enclosed by an Amperian loop.
ampere s law9

Direction of

integration

Ampere’s Law
  • An arbitrary direction for the integration is chosen.
ampere s law10

Direction of

integration

Ampere’s Law
  • The loop is broken into elements of length ds (choose in the direction of the integration).
  • Direction of B doesn’t need to be known before the integration!
ampere s law11

Direction of

integration

Ampere’s Law
  • B can be in an arbitrary direction at some angle to ds as shown (from the right hand grip rule we know B must in the plane of page).
  • We choose B to be in the

direction as ds.

ampere s law12
Ampere’s Law
  • The right hand screw (grip) rule is used to assign a direction to the enclosed currents.
  • A current passing through the loop in the same direction as the thumb are positive ( in the opposite direction -ve).
ampere s law13

Direction of

integration

Ampere’s Law
  • Consider the integral,
ampere s law14

Direction of

integration

Ampere’s Law
  • Applying the screw rule,
ampere s law15
Ampere’s Law
  • Example. Find the magnetic field outside a long straight wire with current.

I

r

ampere s law16

Amperian Loop

Wire surface

Ampere’s Law
  • We draw an Amperian loop and the direction of integration.

Direction of

Integration

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Ampere’s Law
  • Recall,
  • Therefore,
  • The equation derived earlier.
ampere s law18
Ampere’s Law
  • The positive sign for the current collaborates that the direction of B was correct.
ampere s law19

Amperian Loop

Wire surface

Ampere’s Law
  • Example. Magnetic Field inside a Long Straight wire with current.
ampere s law20
Ampere’s Law
  • Ampere’s Law,
ampere s law21
Ampere’s Law
  • Ampere’s Law,
  • The charge enclosed is proportional to the area encircled by the loop,
ampere s law22
Ampere’s Law
  • The current enclosed is positive from the right hand rule.