Physics 6B Magnetic Forces and Fields Prepared by Vince Zaccone For Campus Learning Assistance...

Physics 6B

Magnetic Forces and Fields

Prepared by Vince Zaccone

For Campus Learning Assistance Services at UCSB

What creates a magnetic field?

Answer: MOVING CHARGES

What is affected by a magnetic field?

We have a formula for magnetic force on a moving charge:

)sin(BvqBvqFmag

We have a formula for magnetic force on a moving charge:

)sin(BvqBvqFmag

This is a vector cross-product. We need a right-hand-rule to find the direction of this force.

How to find the direction:0)Use your RIGHT HAND1)Fingers start in the direction of the charge’s velocity.2)Curl fingers toward the direction of the magnetic field.3)Thumb points in the direction of the magnetic force on the charge.4)If the charge is negative, flip your hand over.

Important notes: If velocity is aligned with the magnetic field, force is zero. Magnetic force is always perpendicular to both the velocity and the B-field.

X X X X X X

A uniform magnetic field is directed into the page.

Find the direction of the magnetic force on charge A, a positive charge.

X X X X X X

Find the direction of the magnetic force on charge A, a positive charge.

-Fingers start along A’s velocity (up in the picture)

-Fingers bend toward B-field (into the page)

-Thumb sticks out to the left.magF

X X X X X X

Find the direction of the magnetic force on charge B, a positive charge.

X X X X X X

Find the direction of the magnetic force on charge B, a positive charge.

-Fingers start along B’s velocity (up and to the left in the picture)

-Thumb sticks out down and to the left.

X X X X X X

Find the direction of the magnetic force on charge C, a negative charge.

X X X X X X

Find the direction of the magnetic force on charge C, a negative charge.

-Fingers start along C’s velocity (to the right in the picture)

-Thumb sticks out upward.

-Force is downward. (negative charges are pushed in the opposite direction)

X X X X X X

Now that we can find the force on a charge, we should be able to predict its trajectory.

Notice that the force is always perpendicular to the velocity. This will yield a circular path. In other words, the magnetic force is a centripetal force.

Notice that in this diagram, A is a positive charge, and moves counter-clockwise.

Since B is a negative charge, it moves the opposite direction - clockwise.

So you can tell the sign of the charge by which direction it rotates in a magnetic field.

What path would a neutral charge follow?

X X X X X X

Find the direction of the magnetic force on the wire, with current flowing as shown.

IPretend that positive charges are flowing in the direction of the current.

-Fingers start along A’s current (up in the picture)

-Thumb sticks out to the left.

There is a formula for the force on a wire in a B-field:

)sin(BLIFmag

Length of wire

Application: Torque on a current loop.

The square loop of wire has current I running through it as shown. If a uniform magnetic field passes through the loop it will rotate due to the magnetic forces on the 4 sides of the loop. Note that the net force will be zero, but the loop will spin in an attempt to align itself with the magnetic field (so that the maximum number of field lines pass through the loop).

How can you create a magnetic field?

Answer: move some charges (e.g. make current flow in a wire)

Magnetic Field Near a Long Straight Wire:

R = distance from wire

This formula gives the magnitude of the magnetic field near a wire. The B-field takes the shape of concentric rings centered on the wire.

A right-hand-rule will give the orientation:-Put your thumb along the wire in the direction of the current.-Curl your fingers around the wire (as if you are grasping the wire)-Your fingers are the field lines.

2 current-carrying wires will put magnetic forces on each other.

Wire #1 and #2 below both have current flowing to the right.Find the direction of the magnetic force on each wire.

Wire #1 I1

Wire #2 I2

Wire #1 I1

Wire #2 I2

The magnetic field created by wire #1 is shown. The field points into the page in the vicinity of wire #2, creating magnetic force upward on wire #2.

Wire #1 I1

Wire #2 I2

Now we see the field created by wire #2. The field points out of the page in the vicinity of wire #1, creating magnetic force downward on wire #1.

Wire #1 I1

Wire #2 I2

Basic result:

Parallel curents - wires will attract each other

Anti-parallel currents - wires will repel.

The field near a straight wire is curved into loops.

How can you create a straight magnetic field?

Answer: Bend the wire into a loop (or lots of loops – make a coil of wire).

Magnetic Field in a Solenoid (aka coil)

InB 0 n is the number of loops per meter

Notice the direction of the field – it looks very much like a bar magnet. The B-field lines go in through the south pole and come out through the north pole. Inside the coil the field is nearly uniform and points along the axis.

To find the direction you can use a right-hand-rule:

-Curl your fingers around the coil in the direction of the current.-Stick out your thumb: this is the direction of the B-field inside.

The strength of the field can be increased by inserting an iron core.

Physics 6B Magnetic Forces and Fields Prepared by Vince Zaccone For Campus Learning Assistance...

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