05.4a - Mag Fields

Magnetic fields are produced by moving electric charges and these fields exert forces on other moving charges. We have two main jobs in this chapter:

to understand the sources of magnetic fields (F=qvß) and the patterns (ß) they produce and
to see how to calculate the magnetic force (F=ßIL) on a charged particle.

Shape of magentic fields around magnets

Qualitative: Use the magnetic field demonstrator to investigate the shape of magnetic field around a variety of magnets, as shown.

An online simulation of the magnetic field around a bar magnet can be found here or here or here.

Quantitative: Using a Vernier Magnetic Field Sensor how would you map the field strength of a magnet? Using a process similar to mapping an electric field, create a

Quantitative: Your cell phone has a magnetic field sensor, find an app that will allow you to access these readings. Determine the location of the sensor within your phone. What are the different units that your phone measures the magnetic field?

TO DO:

Determine and Record the FOUR (4) properties of magnetic field lines?

Four Props:

Emerging from the north pole of the magnet to its south pole.
These lines are curved and continuous.
The magnetic field lines are parallel to each other i.e they never intersect each other.
The number of magnetic field line per unit area or magnetic flux is more at the poles, that is the reason why the magnetic field strength is more at poles.

Shape and direction of magnetic fields around current carrying wires

Straight conductor

Physical Materials:

Qualitative: Connect the straight conductor apparatus to an electromagnetic power supply as shown below. Place compasses around the wire. Switch ON the power supply and observe the shape and direction of the magnetic field shown by the compasses. SKETCH THIS PATTERN IN YOUR NOTES.

The wire can be thought to be coming up from one side and down the other. Place the compasses around the other end of the wire and repeat the process from above. SKETCH THIS PATTERN IN YOUR NOTES.

Quantitative: Can you use the Vernier Magnetic Field Sensor to determine both magnitude and direction of the field surrounding the wire?

The picture below shows how the right hand can be used to help determine the shape and direction of the magnetic field around a straight conductor.

Try and work out how this right-hand rule can be used with a straight conductor.

Online Simulation:

An online simulation on the shape and direction of the magnetic field around a straight wire can be found here or HERE.

Set the simulation to the following parameters:
- Field Selection: Current Line
- Display: Field Vectors
- Make Observations.
Check the box for REVERSE
- What is being 'Reversed' by checking this box?
TO DO:
- SKETCH and ANNOTATE THIS PATTERN IN YOUR NOTES.
- Outline the impact of changing the direction of the current (I) on the direction of the magnetic field (ß).
- By using the diagram to the right, suggest how the simulation corresponds with the Right Hand Rule.
- Sketch a hand, label the direction of the Current (I) and the Magnetic Field (ß).

Magnetic Fields in Loops

Loops

Qualitative: Connect the loop apparatus to an electromagnetic power supply as shown. Place compasses around the wire. Switch ON the power supply and observe the shape and direction of the magnetic field shown by the compasses.

Try and work out how the same right-hand rule as above can be used to work out the shape and direction of the magnetic field around a looped conductor.

Quantitative: How would you position the Magnetic Field Sensor to obtain consistent, meaningful data about the size and direction of the magnetic field in both loops?

Repeat for the multiple loop wire as well. How would you indicate/represent the difference in strength between 1 and 5 loops?

Online Simulation:

Using the same simulation, HERE.

Apply these settings:
- Field Selection: Current Loop
- Display: Field Vectors
- Show Z slice
Move the Z-slice through the vertically through the loop.

TO DO:

Sketch and annotate the magnetic field surrounding a current carrying loop.
Based on the MAGNETIC Field Vectors and the Right Hand Rule, DETERMINE the direction of the current in the loop.

Magnetic Fields in Solenoids

Solenoid

Connect the solenoid apparatus to an electromagnetic power supply as shown below. Place compasses inside and around the solenoid. Switch ON the power supply and observe the shape and direction of the magnetic field shown by the compasses.

Try and work out how the same right-hand rule as above can be used to work out the shape and direction of the magnetic field around a solenoid.

An online simulation of the magnetic field around a solenoid can be found here.

Online Simulation:

Using the same simulation, HERE.

Apply these settings:
- Field Selection: Solenoid
- Display: YOUR CHOICE
TO DO:
- Sketch and Annotate the magnetic field within a solenoid.
- Outline how adding multiple coils (solenoid) amplifies the magnetic field with the coils.

Force on a current carrying conductor

Connect the apparatus shown below to a dc power supply. The conductor should sit on top of the metal rails on either side of the magnets.

Switch ON the power supply so that current flows through the conductor and observe the movement of the conductor. Change the direction of the current by swapping the wires to the +ve and -ve sockets and again observe the movement of the conductor.

The direction of the magnetic field of the magnets is upwards, as shown in the diagram above. The direction of the force on the conductor can be determined using the left-hand rule shown below.

If the thumb is used to represent the direction of the force then try and work out which finger can be used to represent the direction of the current and which can be used to represent the direction of the magnetic field.

Quantitative: Is the bar moving with a constant speed or is it accelerating? Devise a method of measuring its motion to support your answer.

An online simulation of this activity can be found here or here.

TO DO:

Sketch and Annotate your hand indicating the direction of the Magnetic Field (ß), the Electric Current (I) and the Force (F).
Outline the impact changing either the orientation of the magnetic field (ß) or the current would have on the movement of the metal rod.

National Magnetic Lab - 45T Super Magnet

Requires FLASH Player

Investigating the relationship between the magnitude of the force and current - PIVOTInteractives Data Collection

Introduction

In this experiment the magnetic field strength of the field between the poles of two attracting magnets will be determined by varying the current through a wire lying in the field.

Apparatus

Wire frame, clamp stand, digital ammeter, power supply, electronic balance, mounted magnadur magnets and C-core.

Instructions

Set up the apparatus as shown in the diagram with the power supply switched OFF.

PIVOT Interactives Magnetic Field Strengths.

Magnet A: 0.2012 T
Magnet B: 0.3424 T
Magnet C: 0.4305 T
Magnet D: 0.4871 T

Set the C-core, with the attached magnets, on the electronic balance.
Suspend the wire frame from a clamp stand in the space between the magnets so that the wire is at right angles to the magnetic field, as shown below.
Measure the length of the wire that is in the magnetic field with a ruler.
Tare the reading on the electronic balance so that it reads zero.
Set the power supply to a small value e.g. 1.0 V and then switch ON the power supply.
Record the ammeter reading and the new reading on the electronic balance.
Calculate the force F exerted on the wire from F = mg, where m is the mass reading from the electronic balance and g is the gravitational field strength. In the example below the current I is 1.64 A and the force F is 3.3 mN or 0.0033 N.
Repeat for a range of values up to a maximum of approximately 4 V from the power supply. Beyond this value the copper wire will become too warm and the circuit breaker will activate.
Plot a graph of force (y-axis) against current (x-axis).
Following the questions on your spreadsheet, determine the quantity stated.

Theory

The force exerted on the wire is related to the current through the wire by the following equation (assuming that the wire is perpendicular to the field),

F = ßxIL sinθ

where L is the length of the wire in the magnetic field, I is the current and ß is the magnetic field strength.

Using the graph of force against current, determine the strength of the magnetic field between the two magnets. The graph should show error bars and the maximum and minimum gradient. The uncertainty in the magnetic field strength should be determined from the graph.

E&M Model Deployment:

using F=qvß or F=ßIL, the RHR or LHR, explain the effect of various magnets or mag fields on the beam of electrons.

Fields in a Solenoid

From the data above, determine the qualitative and quantitative significance of the slope/gradient of the trend line.

Solenoid: 320 Turns

Solenoid: 1340 Turns

Cross Product v. Dot Product

Dot Product: Max @ 0˚ = cosθ

When two vectors are multiplied their product is at a maximum when the vectors are 0˚ / 180˚ towards each other.

Two key examples:

Force and displacement producing work
Force and velocity producing power

Cross Product: Maximum @ 90˚ = sinθ

When the two vectors are multiplied their product is at a maximum when the vectors are at 90˚/270˚ towards each other. Two key examples:

magnetic fields and current / moving charge producing magnetic force.
force and radius producing torque

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