Transcript Magnetic Fields Due To Currents

Magnetic Fields Due To Currents
Law of Biot and Savart
Magnetic Field due to a Long Straight Wire
Magnetic Field due to a Circular Arc of Wire
Force Between Two Parallel Currents
Ampere’s Law
Magnetic Field Inside a Long Straight Wire
Solenoids and Toroids
Current Carrying Coil as a Dipole
pps by C Gliniewicz
A current passing through a wire creates a magnetic field around the wire. This is
known because electromagnets are made by encircling an iron object with coils of
wires. One can imagine some small length of wire, ds, with a current moving
through the wire creating a magnetic field at some point a distance. R, from the wire
at an angle, θ. We can determine the magnetic field element, d.
The quantity, ₀, is called the permeability constant. The value of the permeability
constant is an exact value.
The vector form of the equation for the magnetic field element is called the Law of
Biot and Savart.
The magnetic field due to a long straight wire forms a circle around the wire. The
magnetic field decreases with the radius.
pps by C Gliniewicz
If one grasps a long wire by with the right hand in such a way that the thumb points
in the direction of the positive current flow, then one’s fingers will naturally curl
around the wire, pointing in the direction of the magnetic field. Recall that the
magnetic field points from north to the south pole.
When two parallel wires have current moving through them, one can find the
magnetic field due to one wire at the second wire. Then one can find the force on
the wire due to the current and magnetic field.
One can use the right hand rule to determine the direction of the force by pointing
one’s fingers in the direction of the current and curling them to the direction of the
magnetic field. The thumb then points in the direction of the force. Wires carrying
parallel currents attract one another. Antiparallel currents repel each other.
A rail gun uses this fact to cause a projectile to move at extremely high speeds.
There is a method to determine the magnetic field from the current if symmetry
exists with the object in question.
pps by C Gliniewicz
Ampere’s Law describes how to calculate the magnetic field. Although attributed to
Ampere, this law was actually determined by Maxwell.
The circle on the integral sign means that the scalar product is to be integrated
around a closed loop. If one curls their fingers around the loop in the direction of
integration, then the outstretched thumb points in the direction of the positive
current.
If a wire with a radius, R, has a current flowing through it, there is a magnetic field
inside the wire, but it is only due to the current flowing inside the point in question
at some distance, r, from the center.
A solenoid is a coil of wire whose length is much greater than its diameter. The
number of coils per unit length, n, is used to calculate the magnetic field at the
center of the solenoid.
pps by C Gliniewicz
A toroid is a solenoid which is curled into a donut shape. It creates a magnetic field
at the center of the coils.
The value, N, is the total number of turns in the toroid. In this equation, the radius
is part of the term. That means that the magnetic field inside the wire varies with
the radius, unlike the equation of the solenoid which has a constant magnetic field.
A coil of wire with a current creates a magnetic field and thus can act like a
magnetic dipole. The magnetic field, pointing along the axis of the loop, has a
value
pps by C Gliniewicz