In 1879, graduate student Edwin Hall discovered that if current I flow s through
ID: 1414171 • Letter: I
Question
In 1879, graduate student Edwin Hall discovered that if current I flow s through a conductor in the presence of a magnetic field B, where B is perpendicular to I, charge builds up on the surface of the conductor. In this problem you will explain this phenomenon using what you have learned about electric and magnetic forces. The figure below shows a rectangular conductor in the presence of a magnetic field B pointing into the page. Because there is a current I flowing through the conductor, electrons move through the conductor with average velocity v. What is the direction and magnitude of the magnetic force F_m felt by the electrons? Electrons flowing through the conductor are deflected in the direction of the magnetic force F_m and negative charge accumulates on the top of the conductor, while positive charge (due to the depletion of electrons) accumulates on the bottom of the conductor. The system reaches equilibrium when the force on electrons from the electric field due to the accumulated surface charge balances the magnetic force. W lint is the magnitude of this electric field in terms of B? Assuming a constant electric field inside the conductor (as if it is a parallel plate capacitor), what is the potential difference Delta V between the top and bottom of the conductor (the width of the conductor is w)? This is known as the Hall voltage, and it can be used to measure magnetic fields. For a given magnetic field B and current I, would the Hall effect be different if the charge carriers in conductors were positively charged instead of negatively charged? If so, explain how the effect would be different. Useful equations: F = q(E + v Times B) Delta V = -integral E middot dsExplanation / Answer
a) Fm = q(v x B)
q is -ve , v is to the left and B is into the page.
hence Fm will be upward.
for magnitude =evB
b) electric forec = magnetic force
qE = qvB
E = vB
c) deltaV = E.w = wvB
d) it will be same.
as magnitude of q is same for both/.