Purpose of this Minilab

1. Purpose of this Minilab • Learn about the shape and strength of the magnetic fields created by magnetic dipoles. • Determine the strength of the Earth’s magnetic field.

2. The Concept of “Field” and “Field Lines” The term “field” implies a region of space (or all of space) Each location within this “field” has a specific property. For example: In an “Electric Field” the property at each location in the field is the electric field vector force on a “test charge” charge of the small “test charge”

3. Electric Field of a “Point Charge” Q A location in the field Q

4. Electric “Field Lines” For electric fields, the property at each location in the field is a vector (has direction and magnitude). When connecting the tangents to for different locations we can create a map of “field lines”. Field Lines (tangential to electric field vectors)

5. Electric Field Lines of a “Point Charge” Q Notice: Looking at the “field lines”, you can infer the direction of by looking at the direction of the field lines and, you can infer the strength of by looking at the density of the field lines.

6. Electric Dipoles Electric dipoles consist of two separate point charges. Q1 Q2

7. Electric Dipole Field For two point charges with equal but opposite charge the electric field looks like this:

8. N S S S N N Magnets Magnetic monopoles have never been found:  Magnets have two poles (“North and South poles”) If you cut the magnet in half, each half will still have two poles

9. Magnetic Fields To trace the direction of the magnetic field, a small test magnet (compass) can be used

10. Activity 1: Trace the Magnetic Field of a Horseshoe Magnet Draw on outline of the magnet on the paper. Use compass to map field lines. Draw them on the paper. Tape paper to table.

11. Activity 2: Trace the Magnetic Field of a Bar Magnet Back side has a cutout for the bar magnet Use the cork pin board Insert bar magnet into cutout. Secure with blue masking tape. • - Turn the board around. • - Use pins to secure a sheet of paper. • Trace the field lines of the bar magnet • on the paper using the compass.

12. Activity 3: Field Perturbation Tape steel disc near the magnet at the bottom of the cork board.

13. Part 2: Measure the Earth’s Magnetic Field

14. Theoretical Field due to a Magnetic Monopole

15. Superimpose Two Monopole Fields of Opposite Polarity to Get the Dipole Field Strength Along a Line as Shown D L compass pole #1 pole #2 r1=D r2=D+L

16. Find Distance at which B(D,L) = BEarth D L Determine experimentally as follows using polar graph paper 

17. 0° 45° 90° • Print polar graph paper. • Place compass on graph paper (pivot in center). • Rotate polar paper until compass needle points to 0°.

18. Btotal BEarth Bm • 4) Place bar magnet as shown with its axis in 90° direction. • Move bar magnet until compass needle is deflected by 45°. • At that angle: BEarth=Bm 0° 45° move left or right 90° This is the distance D for which Bm=BEarth .

19. 0° 45° 90° 0° 45° 90° 0° 45° 90° Do this procedure for all 4 possible configurations as shown here. Then get the average distance Dave of these four measurements. 0° 45° 90°

20. Substitute BEarth and Dave into Equation 2

21. The Magnetic Moment of the Bar Magnet L magnetic pole strength magnetic moment of bar magnet

22. Magnetic Moment in an External Magnetic Field B Magnetic moment in external field B experiences a torque that acts to align the magnetic moment with the field. (No torque if magnetic moment is aligned with the field).

23. B B If Magnet is Free to Rotate, an Oscillation Occurs pivot point Torque on magnetrotates magnet towards alignment with the field …..but it overshoots to the other side, like a pendulum…. Once the magnet has reached the other extreme position, it rotates back towards alignment, but will overshoot again….  The magnet oscillates between these two extreme positions.

24. The Period of this Oscillation C A K = m B = p L B B = external magnetic field m = magnetic moment

25. Measuring Period T in Earth’s Magnetic Field ceiling 3.596 s Start/Stop Reset Use stopwatch to measure period T

26. Calculating BEarth Calculated from measurements of M, A, C measured measured measured known Two equations with two unknowns: p, BEarth Solution: Solve first equation for p, then plug result into second equation. Then solve for that equation for BEarth.