General Physics II - Chapter 21: Magnetic Forces and Magnetic Fields

Magnetic Fields

• Magnetism was first discovered in Magnesia, Asia Minor, where rocks could attract each other and were called “magnets.”

• Magnets have two poles: North and South. The magnetic effect is strongest at the poles.

• Similar poles repel each other, while opposite poles attract.

Magnetic Fields Visualization

• Similar to electric fields, magnetic fields can be visualized surrounding a magnet.

• The direction of the magnetic field is the direction a compass needle's north pole would point.

• A compass needle is a bar magnet supported at its center that can rotate freely.

• Magnetic field lines continue inside the magnet.

• The magnetic field (\vec{B}) is a vector quantity measured in Tesla (T).

Magnetic Monopoles

• Cutting a bar magnet in half results in two new magnets, not isolated poles.

• Physicists have searched for single magnetic poles (monopoles), but none have been found.

Earth’s Magnetic Field

• The north pole (N) of a compass needle points to the Earth’s north geographic pole, where the Earth’s south magnetic pole is located.

• Earth's magnetic poles do not align with its geographic poles.

• Magnetic declination is the angular difference between a compass needle's direction and true north (varies from 0° to about 20°).

• Earth’s magnetic field is thought to be produced by electric currents in the Earth’s molten iron outer core.

Electric Currents and Magnetic Fields

• Hans Oersted (1777–1851) discovered that a compass needle deflects when placed near a wire carrying an electric current (\vec{I}). The magnetic field lines produced by the current in a straight wire are circles centered on the wire.

• Right-hand rule (1) determines the magnetic field direction:

  • Grasp the wire with your right hand, thumb pointing in the current direction.

  • Your fingers encircle the wire in the direction of the magnetic field.

• Symbol ⨀ represents current pointing toward you (out of the page).

• Symbol ⨂ represents current pointing away from you (into the page).

Magnetic Field of a Straight Wire

• The magnetic field (\vec{B}) due to the current in a long straight wire is directly proportional to the current (\vec{I}) and inversely proportional to the distance (\vec{r}) from the wire:
  
  B \propto \frac{I}{r}

• The proportionality constant is \frac{\mu0}{2\pi}, where \mu0 is the permeability of free space (\mu_0 = 4\pi \times 10^{-7} T⋅m/A).

• The magnetic field magnitude is given by:
  
  B = \frac{\mu_0 I}{2\pi r}

Magnetic Field of a Wire Loop

• The magnetic field produced by a current in a wire loop at the loop center (\vec{P}) is given by:
  
  B = \frac{\mu_0 I}{2R}
  Where R is the loop radius and I is the current.

Magnetic Force on an Electric Current

• Magnets exert a force on current-carrying wires.

• For a straight wire placed in a magnetic field (\vec{B}), the force direction is perpendicular to both the current and the magnetic field.

• Right-hand rule (2): Orient your right hand in the current direction (\vec{I}), bend fingers toward magnetic field lines (\vec{B}). Your thumb points toward the force on the wire.

• Magnitude of the force is:
  
  F_B = I\ell B \sin(\theta)
  Where I is the current, B is the magnetic field, \ell is the wire length, and \theta is the angle between the current and magnetic field directions.

• If I and B are perpendicular, then FB = I\ell B, and if parallel, then FB = 0.

• SI unit of magnetic field B is Tesla (T): 1 T = 1 N/(A⋅m).

• The cgs unit for magnetic field is the gauss (G): 1 G = 10^{-4} T.

Force Between Two Parallel Wires

• Two long parallel wires separated by distance d, carrying currents I1 and I2, exert a force on each other.

• Each current produces a magnetic field

Equations, Physical Quantities, and Units