A thick metal slab carries a current I as shown. A uniform magnetic field B points perpendicular to the slab (and into the page). If point P on the slab is at a higher potential than point Q , what can we say about the charge carriers that produce the current in the slab?
a.They are positive.
b. They are negative.
c.They could be either positive or negative, but we can't tell without more information.
d.The situation is impossible: point could never be at a higher potential than point , no matter what the sign of the charge carrier.
To determine the answer, we need to understand how the potential difference is related to the current flow and the magnetic field. The potential difference between two points in a conductor is given by the formula:
V = B * L * Vd * I
where V is the potential difference, B is the magnetic field strength, L is the length of the conductor (in this case, the thickness of the slab), Vd is the drift velocity of the charge carriers, and I is the current.
If point P is at a higher potential than point Q, it means that the potential difference (V) is positive. According to the above formula, for V to be positive, the product (B * L * Vd) should also be positive. Since we know that both B and L are positive quantities, the sign of Vd determines the sign of the charge carriers.
If Vd is positive, it means that the charge carriers are moving in the direction opposite to the current flow. In other words, they are negative charge carriers (electrons). Therefore, the answer is b. They are negative.
It is important to note that this conclusion is based on the assumption that the conventional current direction is taken as the direction of positive charge carriers. If the opposite convention is used, i.e., considering the direction of electronic current flow as the direction of positive charge carriers, then the answer would be a. They are positive charge carriers.