Sources of Magnetic Field
Prepared by:
Ramon P. Velasco, REE, MS Math
Sources of Magnetic Field
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1. Moving Charges
2. Current Element
3. Long Straight Conductor
4. Circular Current Loop
Moving Charge: Magnetic Field Lines
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Where
B is the magnetic field (T)
v is the velocity of the charge (m/s)
q is the charge in Coulomb
r is the distance of the Charge to the point of
consideration in m
• ∅ is the angle between the direction of velocity
and the point of consideration.
• 𝜇o is the of permeability of free space (T-m/A)
Illustrative Example
Magnetic Field of Current Element
• The total magnetic field caused by several
moving charges is the vector sum of the fields
caused
by
the
individual
charges.
(superposition)
Law of Biot and Savart (Bee-oh and
Suh Var)
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Where
B is the magnetic field (T)
I is the current flowing in the current element (A)
L is the length of the current element in meter
r is the distance of the of consideration in m
∅ is the angle between point of consideration and
the conductor
• 𝜇o is the of permeability of free space (T-m/A)
Magnetic Field of a Long Straight
Conductor
• Where
• B is the magnetic field (T)
• I is the current flowing in the current element
(A)
• r is the distance of the of consideration in m
• 𝜇o is the of permeability of free space (T-m/A)
Force Between Parallel Conductor
• F= BIL
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Where
B is the magnetic field (T)
Ii is the current flowing in the first conductor
I2 is the current flowing in the second
conductor
• r is the distance of conductor in m
• 𝜇o is the of permeability of free space (T-m/A)
Problem Set
Objectives
• 1. Amperes Law
• 2. Solenoid
• 3. Toroid
Ampere’s Law
Illustrative Example
Solenoid
• A long straight coil of wire can be used to
generate a nearly uniform magnetic field
similar to that of a bar magnet. Such coils,
called solenoids, have an enormous number
of practical applications.
Solenoid
Inside the solenoid near the center
Illustrative Example 1.
Toroid
Problem Set
Field at the current of the loop
Field at the current of the loop
Illustrative Example