Lorentz Force Law and Right Hand Rules

• We can use our magnet to move (or change the velocity) of bits of metal

• If we apply a current (by connecting a battery) we can create an electromagnet that did the same thing.

Recall Newton's law that an object will remain at rest unless acted on by an outside force, so the magnet and the electrical current must be generating some kind of force.

Lorentz Force• Lorentz force is the force experienced by a charge moving in

an electromagnetic field.

• Lorentz force is determined by the formula F = qv x B

– q is the magnitude of the charge(Coulomb)

– v is the velocity (m/s)

– B is the magnetic field density. (Tesla)

• Lorentz force is perpendicular to both velocity and magnetic field. The right hand rule is applied when determining Lorentz force.

The x represents a process called a vector cross-product in which qv is perpendicular to B and both are

perpendicular to F.

The three quantities I,B and F and all at right angles to each other. This is called "orthogonal".

I

B F

Begin by lining your thumb up with the current. Then rotate your hand to line your finger with the magnetic field. The direction of your palm is the direction of the force on the wire.

http://www.youtube.com/watch?v=_X8jKqZVwoI

Representing Vectors in Three Dimensions

Motion comes in three pairs of directions:

Left Right

Up Down

Into page Out of page

up

down

left right

out

in

Electrons, electron current flow or anything negative left hand

Protons, conventional current flow or anything positive right hand.

We will use conventional current p+ and right hand rules.

Conventions for Flowing Current or Electric Charge

Marking Up your Hand

Draw a I for current on your thumb

Draw an B for magnetic field on your index finger

Draw a F for force on your palm

I F

B

http://www.youtube.com/watch?v=LK7hv4LX3ys&feature=related&safe=active

The first set of rules is for a moving charge in an EXTERNAL magnetic field (We ignore the field generated by the moving electrons).

The last set of rules is for the magnetic field generated BY the electrons moving around a wire itself.

Force on a wire resulting from a magnetic field

Begin by lining your thumb up with the current. Then rotate your hand to line your finger with the magnetic field. The direction your palm is the direction of the force on the wire.

You can start with any of the other fingers, depending on what you are given in the question, by lining up one finger and rotating the second until it lines up properly. The palm will be pointed in the correct direction.

I F

B

Examples: Movement in an EXTERNAL Magnetic Field

Find the direction of the current, the magnetic field and the Lorentz Force.

N

S

Assume the current in the wire is conventional flow (+ve).

p+ = _____

B = ______

F = ______

out of pagedown - from N pole to S pole so B is downRight - Align my thumb with current, rotate my fingers to align with B (down) and my palm faces to the right

Examples

Find the direction of the current, the magnetic field and the Lorentz Force.

N

S

Assume the current in the wire is conventional flow (+ve).

p+ = _____

B = ______

F = ______

out of pageup -from N to S so B is up

Left -Align my thumb with current, rotate my fingers to align with B (up) and my palm faces to the left

Examples

Find the direction of the current, the magnetic field and the Lorentz Force.

Assume the current in the wire is conventional flow (+ve).

p+ = _____

B = ______

F = ______

out of page

to the right

Down -Align my thumb with current, rotate my fingers to align with B (out of page) and my palm faces down

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p+

We can use a compass to determine the direction of the Magnetic field in the wire or we can use the "Wire-wrap Rule"

"Wire-Grasp" Rule for the Magnetic Field Generated BY the Wire

Recall that the magnetic field lines around a wire form circles around the wire.

For conventional current

Using the "Wire-Grasp" Rule for the Magnetic Field Generated BY the Wire

• Line your thumb up with the direction of the conventional current flowing in the wire (+ve).

• Imagine you are curling your fingers around the wire.

• Your fingers point in the direction the magnetic field is pointing. (Up on one side of the wire and down on the other.

Don't use this rule if there is an external applied field.

Example: Consider the following current carrying wires. Draw the magnetic fields generated by the wires.

p+p+

a) Straight wire b) Current in a loop of wire

Solenoids

• A solenoid is a long coil of thin wire, which when wrapped around a piece of metal, produces a magnetic field when an electric current is passed through it.

• Solenoids are important because they can create controlled magnetic fields and can be used as electromagnets.

Coils of wire

Polarity of a solenoid

Method 1:

To find the polarity of a solenoid point your fingers in the direction of the conventional current as it enters the solenoid. Your thumb will point in the direction of N-pole of the solenoid.

Method 2:

To find the polarity of a solenoid, we use the clock rule. Remember the mnemonic.....

aNticlockwise = North Pole

clockwiSe = South Pole

Face the end of the solenoid. If the direction of current is anticlockwise from your end, it is the North Pole, else, if clockwise it is the south pole

Example

p+

current is moving clockwise => South pole

Polarity of a Magnet

Curl your fingers around the wire with your thumb pointing in the direction of the conventional current (flow of +ve charge). Your thumb points to the North end of the solenoid.

Left hand Rules-Use when there is a negative charge flow

Forces on a Current Carrying Wire

Lorentz Force on a WireFor a single charge the force it will experience in an external magnetic field is given by:

F = qv x B

Only that portion of the velocity vector that is perpendicular to the magnetic field will contribute to the force.

The implications of this expression include:

• The force is perpendicular to both the velocity v of the charge q

• and the magnetic field B.

• The magnitude of the force is F = qvB sinθ where θ is the angle <

• 180 degrees between the velocity and the magnetic field.

• This implies that the magnetic force on a stationary charge or a

• charge moving parallel to the magnetic field is zero.

• The direction of the force is given by the right hand rule. The force

• relationship above is in the form of a vector product.

Magnetic Force on a Current Carrying Wire

• If a wire carrying a current is placed in a magnetic field each of the charges moving in the wire will experience a magnetic force along the length of the wire that is in the field.

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current

LB is out of the page

F

L = the length of wire in the magnetic field

I = conventional current (+ve)

Finding the Force Equation

F = q v B sinθ

= q (L/t)B sinθ

= (q/t)L B sinθ

= ILBsinθ

F = BILsinθ

F = BILsinθ

The magnitude of the force is proportional to the current I, the

magnetic field, B and the length of the wire that is in the magnetic

field. θ is the angle between the current and the direction of the

magnetic field.

Use the RHR to find the direction of the Force.

Deriving units for BF= ILBsinθ

B = F/IL

= N/A m

A = 1C/s

Example 1

A power line carries a current of 1.54 x 103 A in Greenland at a spot where the magnetic field is 5.60 x 10-5 T. The power line makes an angle of 36o to the field. What is the magnitude of the Force on a 220 m length of the wire?

Example 2:

A 10.0 cm wire carries a current of 5.0 A. The wire is at right angles to the uniform magnetic field. The force on the wire is 2.0 N. What is the magnitude of the magnetic field?

Example 3:

In March 1967, a 1000T magnetic field was obtained in a lab for a fraction of a second. (The maximum sustained field is about 45T.) If a 25 cm wire is perpendicular to a 1 x 103 T magnetic field and the magnetic force on the wire is 1.6 x 102 N, what is the current?

Why does the wire move?

When a current-carrying conductor is placed in a magnetic field, the interaction between the two magnetic fields will produce a net force on the conductor.

The interaction of the two magnetic fields (the magnetic field of the current-carrying wire and the magnetic field of the permanent magnet) produces a resultant that is the vector sum of the two fields.

This sum produces a non-uniform field that moves the wire from the stronger field to the weaker field

Strength of the Force

The strength of the force can be increased by:

• >Increase the current • >Using a stronger magnet

Assignment

Read/Study pages 19-24

Complete

25 and 26

page 29

page 34

and q.1-17 on page 17