Electricity

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Electricity Magnetism

• Seb Oliver
• Lecture 15
• Examples of Biot-Savart Law

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Summary Lectures 14 15

• Biot-Savart Law
• (Field produced by wires)
• Centre of a wire loop radius R
• Centre of a tight Wire Coil with N turns
• Distance a from long straight wire
• Force between two wires
• Definition of Ampere

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Using the Biot-Savart Law

• Example 1
• A wire loop

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Examples of using the Biot-Savart Law

• Some examples are quite hard and show how
  difficult it is to use this Law
• In a real situation you might use a computer to
  calculate the magnetic field due to the wire
• Next week we will discover Amperes Law which is
  often much easier to use

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Magnetic Field from a Current Loop
Direction
Magnitude
B is always out of screen
ds is always ? to r
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Using the Biot-Savart Law

• Example 2
• A tight coil

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Magnetic Field from a tight coil I.e. many
current loop
Direction
Magnitude
as for a single loop
1 loopCurrent I
N loops Current ? NI
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Using the Biot-Savart Law

• Example 3
• A long Straight wire

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Magnetic Field from a Straight wire
r
a
q
x
ds
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Magnetic Field from a Straight wire
Magnitude
Direction
B is always out of screen
It turns out it is easier if we get everything in
terms of q
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Magnetic Field from a Straight wire
Magnitude
Now we have to use calculus!
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Other examples of Magnetic field

• Centre of a wire loop radius R
• Centre of a tight Wire Coil with N turns
• Distance a from long straight wire

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Magnetic Force Between Two Parallel Wires
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Magnetic Force Between Two Parallel Wires

• A current carrying wire in a magnetic field feels
  a magnetic force
• A current carrying wire generates a magnetic
  field
• Thus two current carrying wires will exert a
  force on each other

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Magnetic Force Between Two Parallel Wires
I1
a
Magnetic field at wire 1 from wire 2
I2
B2
Magnetic Force on wire 1 due to B2 (everything ?)
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Magnetic Force Between Two Parallel Wires
Force on wire 1 due to wire 2
From Newtons 3rd Law ( symmetry) Force on wire
2 due to wire 1
Force / unit length
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Definition of Ampere
If the magnitude of the force per unit length
between 2 parallel wires carrying identical
currents and separated by 1m is 210-7 N/m then
the current in each wire is 1A
Definition of a Coulomb If a current of 1A is
passing through a wire then 1C of charge passes a
surface in 1s
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Quiz

• I1 2A, I2 6A
• (a) F1 3F2
• (b) F1 F2
• (c) F1 F2/3

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Summary Lectures 14 15

• Biot-Savart Law
• (Field produced by wires)
• Centre of a wire loop radius R
• Centre of a tight Wire Coil with N turns
• Distance a from long straight wire
• Force between two wires
• Definition of Ampere