• Magnets and the magnetic field

• Electric currents create magnetic fields

• Magnetic fields of wires, loops, and solenoids

• Magnetic forces on charges and currents

• Magnets and magnetic materials

Chapter 24Magnetic Fields and Forces

Topics:

Sample question:This image of a patient’s knee was made with magnetic fields, not x rays. How can we use magnetic fields to visualize the inside of the body?

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Key Points• Three types of magnetic interactions

1. no interaction with either pole of a magnet => object is non-magnetic

2. attracted to both poles of a magnet => object is magnetic

3. Attracted to one pole and repelled by the other pole=> object is a magnet

• Magnetic field vector from a bar magnet is a super position of the magnetic field vectors from the N and S poles:

• Vector from N pole points away from N pole

• Vector from S pole points towards S pole

• Field lines form complete loops inside and outside of magnet• Field lines outside magnet go from N to S poles

• Field lines inside magnet go from S to N poles

• Magnetic Field vectors at a point are tangential to Magnetic Field Lines

3-D Arrows, Cross Products, and Right Hand Rule 1

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• Showing vectors in 3D

• Cross Product

For direction use Right-hand rule 1

• Right-hand rule 1 (RHR 1) => for finding direction of cross-product vector

(Cross-Product Rule)1.Point right hand in the direction of the first vector (vector A)

2.Rotate your right hand until you can point your fingers in the direction of the second vector (vector B)

3.Thumb points in direction the cross-product vector (vector C)

Right Hand Rules for Magnetism

• Right-hand rule 1 (RHR 1) => for finding magnetic forceFB= q*v_vector x B_vector (Cross-Product Rule)

1. Point right hand in the direction the charges are moving (current or velocity)

2. Rotate your right hand until you can point your fingers in the direction of the magnetic Field

3. Thumb points in direction of force for + chargeForce is in opposite direction for - charges

• Right-hand rule 2 (RHR 2) => Finding direction of B from I• Point thumb of right hand in direction of current I,

• B-field lines curl in direction of fingers

• Right-hand rule 3 (RHR 3) => Finding direction of current in a loop from direction of B-field

• Point thumb of right hand in direction of B-field

• Fingers of right hand curl in direction of current

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Drawing Field Lines of a Bar Magnet

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Magnetic Fields Produced by Bar Magnets

A single bar magnet A single bar magnet(closeup)

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Magnetic Fields Produced by Bar Magnets

Two bar magnets, unlike poles facing

Two bar magnets,like poles facing

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Magnetic Fields from Two MagnetsBar Magnets A and B are placed at right angles. Two compasses, X and Y are placed so that they are equidistant from the two magnets as shown

A.) The arrow in compass X indicates the direction in which the North pole of the compass is pointing. Indicate the North and South ends of both magnets in the diagram

B.) Draw an arrow in compass Y to show the direction in which the North pole of the compass needle would point.

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Electric Currents Also Create Magnetic Fields

A long, straight wire

A current loop A solenoid

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The Magnetic Field of a Straight Current-Carrying Wire

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Representing Vectors and Currents That Are Perpendicular to the Page

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Checking Understanding

Point P is 5 cm above the wire as you look straight down at it. In which direction is the magnetic field at P?

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Answer

Point P is 5 cm above the wire as you look straight down at it. In which direction is the magnetic field at P?

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Drawing Field Vectors and Field Lines of a Current-Carrying Wire

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Drawing a Current Loop

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The Magnetic Field of a Current Loop

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The Magnetic Field of a Solenoid

A short solenoid A long solenoid

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The Magnitude of the Field due to a Long, Straight, Current-Carrying Wire

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Checking Understanding

A. 10 A to the right.

B. 5 A to the right.

C. 2.5 A to the right.

D. 10 A to the left.

E. 5 A to the left.

F. 2.5 A to the left.

The magnetic field at point P is zero. What are the magnitude and direction of the current in the lower wire?

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E. 5 A to the left.

The magnetic field at point P is zero. What are the magnitude and direction of the current in the lower wire?

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Answer

The Magnetic Field of a Current Loop

Magnetic field at the center of a current loop of radius R

Magnetic field at the center of a current loop with N turns

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Example

What is the direction and magnitude of the magnetic field at point P, at the center of the loop?

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The Magnetic Field Inside a Solenoid

Magnetic field inside a solenoid of length L with N turns.

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