User talk:Albert FrankEinstein

Hall Effect

The Hall effect is a phenomenon that describes why charged particles collect to one side of a conductor in the presence of a magnetic field. It is used to determine the charge of a mobile particle inside a conductor.

Main Idea

The Hall Effect is a phenomenon that is created when charged particles moving through a conductor are submitted to a magnetic field. The magnetic field pushes the charged particles to one side of the conductor. This causes a buildup of charges on one side of the conductor which creates a polarization of the conductor perpendicular to the current flow. Eventually this charge will stabilize as the mobile charges will resist the magnetic field.

Part 1: Normal circuit (No Magnetic Field Yet)

(For simplicity, the mobile charges have already been determined to be negatively charged electrons. This will not always be the case and it should not be assumed that the mobile charges are electrons)

Mobile electrons flow through a wire due to a parallel electric field inside the wire. This electric field is caused by an energy source such as a battery or power supply. The parallel electric field flows from an area of high potential (i.e. the positive end of the battery) to an area of low potential (i.e. the negative end of the battery). This is the same direction as the conventional current. Since electrons are negatively charged, they flow in the opposite direction of the parallel electric field. This can be summarized by the equation:

Part 1: Normal circuit (No Magnetic Field Yet)

(For simplicity, the mobile charges have already been determined to be negatively charged electrons. This will not always be the case and it should not be assumed that the mobile charges are electrons)

Mobile electrons flow through a wire due to a parallel electric field inside the wire. This electric field is caused by an energy source such as a battery or power supply. The parallel electric field flows from an area of high potential (i.e. the positive end of the battery) to an area of low potential (i.e. the negative end of the battery). This is the same direction as the conventional current. Since electrons are negatively charged, they flow in the opposite direction of the parallel electric field. This can be summarized by the equation:

Part 2: Initial Transient State (Magnetic Field Present)

Mobile electrons are subjected to a magnetic field as they flow through the wire. Since electrons are negatively charged, they experience a magnetic force in the downward direction due to the magnetic field. This can be summarized by the equation:

See aside for extra help on determining this direction.

Part 3: Steady State (Magnetic Field Still Present)

Over time more and more charges are going to build up. As they build up, they will begin to create a charged area on one surface of the conductor. This charged surface will start to oppose the magnetic force that is holding the electrons. Essentially the electrons are being held against the side of the conductor by the magnetic force. As more and more electrons collect together against the surface of the conductor, they start to oppose the magnetic force that’s holding them. This opposing force is called the transverse electric force and is responsible for the existence of the perpendicular electric field. When enough electrons have collected, their combined transverse electric force will be equal in magnitude to the magnetic force that is holding them. At this point, there is no net vertical force pushing more electrons against the surface of the conductor and these electrons will flow normally again. This is called the steady state. As long as the magnetic field remains the same magnitude and in the same direction and the same number of electrons remain pushed against the conductor’s surface, the steady state will be maintained.

Aside: Right Hand Rule

ASIDE: The Right Hand Rule is necessary to use in determining the direction that the magnetic force will point. This is also a great trick to determine the answer to other cross products used in the physics course. First, take your right hand and point your thumb in the direction that the mobile charges are flowing. In this case, this would be the direction that the electrons are flowing. Now with your thumb in that direction, point your index finger in the direction of the magnetic field (in this case, the magnetic field would point in into the page as is shown). Now the most important part; point the rest of your fingers so they are coming straight out of your palm. These fingers are pointing in the direction of the magnetic force FOR A POSITIVE CHARGE. Since we have electrons, the magnetic force will point in the exact opposite way. THIS LAST PART IS EXTREMELY IMPORTANT TO REMEMBER. If it makes it easier, you can do the same technique that was used for the right hand with your left hand anytime you have a negative charge.