Magnets and Magnetic

Fields

Magnetic Field Lines• Never will intersect with each other or cross• Always directed away from the north pole and

towards the south pole of a magnet• Strongest field where the lines are closest

together

Magnetic Force on a Current

• An electric field in a wire moves the electrons through the wire and generates a current

• The moving electrons react to the presence of an external magnetic field:

o F = Force (N)o I = current (A)o L = length of wire within the magnetic field (m)o B = Magnetic Field Strength (T)o q = Angle between the current and the magnetic Field

Right-Hand Rule (a)• To determine the direction of the force that a

current-carrying wire experiences when placed in an existing magnetic field:

o Thumb = direction of currento Pointer finger = direction of fieldo Middle finger = direction of force

Sample problem:• A 12.5 cm long wire with a current of 0.505 A is

placed in a uniform magnetic field of strength 0.850 T. If the current is running towards the right, and the magnetic field is directed into the page (away from you), what is the force it experiences (magnitude and direction)?

Magnetic Force on a Moving Charge

• Currents are made of many, many multiple moving charges.

• Single charged particles that are moving ALSO experience a force:

o F = Force (N)o q = charge (C)o v = velocity of the moving charge (m·s-1)o B = Magnetic Field Strength (T)o q = Angle between the charge’s path and the

magnetic Field

Right-Hand Rule (b)• Same as the rule for a current-carrying wire in a

magnetic field, with the following modification:

• The “current” becomes the direction of the moving positive test charge

What happens when…A charged particle enters a magnetic field?• In what direction is the force?• What does the path become?

Ørsted’s Discovery• A current in a straight long wire produces a

magnetic field around it

• The magnitude of the magnetic field created by the current in a wire varies linearly with the current in the wire and inversely with the perpendicular distance from the wire:

• m0 = magnetic permeability of the vacuum

= (exact number!)

𝐵=𝜇0 ∙ 𝐼2𝜋𝑟

Magnetic Field Strength

• Tidbits of Tesla-related trivia

• The field strength of the Earth at its surface is ~ 10-4 T

• A wire carrying 2000A produces a magnetic field of 8 x 10-5 T 5 m from the wire!

Force BETWEEN two current-carrying wires

• L = length of the wires (m)• r = distance separating the two wires (m)• I = current in the wire• m0 = magnetic permeability of the vacuum

• Assumption is that the wires are parallel to each other

𝐹=𝜇0 𝐼 1 𝐼 2𝐿2𝜋 𝑟

Magnetic Field Patterns

• Around 2 wires with currents in the SAME direction: