Physics 2225: Magnetic Fields 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.

Physics 2225: Magnetic Fields 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 charge of the small “test charge” force on a “test charge”

Physics 2225: Magnetic Fields Electric Field of a “Point Charge” Q Q A location in the field

Physics 2225: Magnetic Fields 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)

Physics 2225: Magnetic Fields 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.

Physics 2225: Magnetic Fields Electric Dipoles Electric dipoles consist of two separate point charges. Q1Q1 Q2Q2

Physics 2225: Magnetic Fields Electric Dipole Field For two point charges with equal but opposite charge the electric field looks like this:

Physics 2225: Magnetic Fields Magnets Magnetic monopoles have never been found:  Magnets have two poles (“North and South poles”) S N If you cut the magnet in half, each half will still have two poles S N S N

Physics 2225: Magnetic Fields Magnetic Fields To trace the direction of the magnetic field, a small test magnet (compass) can be used

Physics 2225: Magnetic Fields Activity 1: Trace the Magnetic Field of a Horseshoe Magnet Tape paper to table. Use compass to map field lines. Draw them on the paper. Draw on outline of the magnet on the paper.

Physics 2225: Magnetic Fields Activity 2: Trace the Magnetic Field of a Bar Magnet Use the cork pin board Back side has a cutout for the bar magnet 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.

Physics 2225: Magnetic Fields Activity 3: Field Perturbation Tape steel disc near the magnet at the bottom of the cork board.

Physics 2225: Magnetic Fields Part 2: Measure the Earth’s Magnetic Field

Physics 2225: Magnetic Fields Theoretical Field due to a Magnetic Monopole

Physics 2225: Magnetic Fields Superimpose Two Monopole Fields of Opposite Polarity to Get the Dipole Field Strength Along a Line as Shown pole #1 pole #2 L compass D r 1 =D r 2 =D+L

Physics 2225: Magnetic Fields Find Distance at which B(D,L) = B Earth L D Determine experimentally as follows using polar graph paper 

Physics 2225: Magnetic Fields 1)Print polar graph paper. 2)Place compass on graph paper (pivot in center). 3)Rotate polar paper until compass needle points to 0°. 0°0° 90° 45°

Physics 2225: Magnetic Fields 4) Place bar magnet as shown with its axis in 90° direction. 5)Move bar magnet until compass needle is deflected by 45°. At that angle: B Earth =B m 0°0° 90° 45° move left or right This is the distance D for which B m =B Earth. B Eart h BmBm B total

Physics 2225: Magnetic Fields Do this procedure for all 4 possible configurations as shown here. Then get the average distance D ave of these four measurements. 0°0° 90° 45° 0°0° 90° 45° 0°0° 90° 45° 0°0° 90° 45°

Physics 2225: Magnetic Fields Substitute B Earth and D ave into Equation 2

Physics 2225: Magnetic Fields The Magnetic Moment of the Bar Magnet L magnetic moment of bar magnet magnetic pole strength

Physics 2225: Magnetic Fields 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).

Physics 2225: Magnetic Fields If Magnet is Free to Rotate, an Oscillation Occurs B B Torque on magnet rotates magnet towards alignment with the field …..but it overshoots to the other side, like a pendulum…. pivot point 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.

Physics 2225: Magnetic Fields The Period of this Oscillation K = m B = p L B A C m = magnetic moment B = external magnetic field

Physics 2225: Magnetic Fields Measuring Period T in Earth’s Magnetic Field ceiling s Start/Stop Reset Use stopwatch to measure period T

Physics 2225: Magnetic Fields Calculating B Earth Two equations with two unknowns: p, B Earth Solution: Solve first equation for p, then plug result into second equation. Then solve for that equation for B Earth. measured known measured Calculated from measurements of M, A, C measured