Magnetic Force
The Magnetic Field
● The vector field is often
represented with magnetic field lines
● field lines point away from N, toward S
● line density shows field strength
Magnetic Forces on Current-Carrying Wires
There’s no force on a current
moving parallel to a magnetic field.
Magnetic Forces on Current-Carrying Wires
For current I :
Magnetic Forces on Current-Carrying Wires
the force on one moving charge
Number of charges in length :
Magnetic Forces on Current-Carrying Wires
The horizontal wire can be levitated—held up against the force of gravity—if the current in the wire is
A. Right to left.
B. Left to right.
C. It can’t be done with this magnetic field.
Magnetic Forces on Current-Carrying Wires
The horizontal wire can be levitated—held up against the force of gravity—if the current in the wire is
A. Right to left.
B. Left to right.
C. It can’t be done with this magnetic field.
Magnetic Forces on Current-Carrying Wires
Magnetic Moment
Define the “magnetic moment”:
Where I is the current and A is
the area, with direction given by the direction of circulation of
the current:
A current loop creates a dipole field.
Magnetic Moment
Define the “magnetic moment”:
A current loop creates a dipole field.
For N loops of wire, the magnetic moment becomes
Torque on a Current Loop
A current loop in a magnetic field experiences a torque.
Torque on a Current Loop
Torque on a Current Loop
A magnetic moment
(such as a current loop) in a B field feels a torque
Torque on a Current Loop
Electric motor:
Torque on a Current Loop
Electric motor:
In 1819 Hans Christian Oersted discovered that an electric current in a wire causes a compass to turn.
Sources of Magnetic Fields
The right-hand rule determines the orientation of the compass needles to the direction of the current.
Sources of Magnetic Fields
• A current-carrying wire produces a magnetic field
• The compass needle deflects in directions tangent to the circle
Sources of Magnetic Fields
• A current-carrying wire produces a magnetic field
• The compass needle deflects in directions tangent to the circle
Sources of Magnetic Fields
A proton is shot straight at the center of a long, straight wire carrying current into the screen. The proton will
A. Go straight into the wire.
B. Hit the wire in front of the screen.
C. Hit the wire behind the screen.
D. Be deflected over the wire.
Sources of Magnetic Fields
A proton is shot straight at the center of a long, straight wire carrying current into the screen. The proton will
A. Go straight into the wire.
B. Hit the wire in front of the screen.
C. Hit the wire behind the screen.
D. Be deflected over the wire.
Sources of Magnetic Fields
v ×B points out of the screen
Sources of Magnetic Fields
Sources of Magnetic Fields
field of a single moving charge
Sources of Magnetic Fields
positive charge moving right
Sources of Magnetic Fields
negative charge moving right
The magnetic field of a charged particle q moving with velocity v is given by the Biot-Savart law:
Sources of Magnetic Fields
Sources of Magnetic Fields
The constant μ0 in the Biot-Savart law is called the permeability constant:
μ0 = 4π × 10–7 T m/A = 1.257 × 10–6 T m/A The constant μ0 is often found in the fraction
