1. The Hall Effect AP Physics Montwood High School R.Casao

2. When a current-carrying conductor is placed in a magnetic field, a voltage is generated in a direction perpendicular to both the current and the magnetic field. The Hall Effect results from the deflection of the charge carriers to one side of the conductor as a result of the magnetic force experienced by the charge carriers. The arrangement for observing the Hall Effect consists of a flat conducting strip carrying a current I in the x-direction.

3. A uniform magnetic field B is applied in the y-direction. If the charge carriers are electrons moving in the negative x-direction with a velocity v d, they will experience an upward magnetic force F B. The electrons will be deflected upward, making the upper edge negatively charged and the lower edge positively charged.

4. The accumulation of charge at the edges continues until the electric field and the resulting electric force set up by the charge separation balances the magnetic force on the charge carriers (F mag = F electric ). When equilibrium is reached, the electrons are no longer deflected upward.

5. A voltmeter connected across the conductor can be used to measure the potential difference across the conductor, known as the Hall voltage V H. When the charge carriers are positive, the charges experience an upward magnetic force q·(v x B).

6. The upper edge of the conductor becomes positively charged, leaving the bottom of the conductor negatively charged. The sign of the Hall voltage generated is opposite the sign of the Hall voltage resulting from the deflection of electrons. The sign of the charge carriers can be determined from the polarity of the Hall voltage. When equilibrium is reached between the electric force q·E and the magnetic force q·v d ·B, the electric field produced between the positive and negative charges is referred to as the Hall field, E H, therefore, q·E H = q·v d ·B.

7. E H = v d ·B If d is taken to be the width of the conductor, then the Hall voltage V H measured by the voltmeter is: The measured Hall voltage gives a value for the drift velocity of the charge carriers if d and B are known.

8. The number of charge carriers per unit volume (charge density), n, can also be determined by measuring the current in the conductor: Area A = thickness t·d, therefore:

9. Hall coefficient, R H = The Hall coefficient can be determined from The sign and magnitude of R H gives the sign of the charge carriers and their density. In most metals, the charge carriers are electrons and the charge density determined from the Hall effect measurements agrees with calculated values for metals which release a single valence electron and charge density is approximately equal to the number of valence electrons per unit volume.

10. Legend: 1.Electrons (not conventional current) 2. Hall element, or Hall sensor 3. Magnets 4. Magnetic field 5. Power source In drawing "A", the Hall element takes on a negative charge at the top edge (symbolized by the blue color) and positive at the lower edge (red color). In "B" and "C", either the electric current or the magnetic field is reversed, causing the polarization to reverse. Reversing both current and magnetic field (drawing "D") causes the Hall element to again assume a negative charge at the upper edge.