Calculate speed v in crossfield hall effect

[th3plan]

Homework Statement

metal strip 6.66 cm long, 1.11 cm wide, and 0.837 mm thick moves with constant velocity through a uniform magnetic field B = 1.55 mT directed perpendicular to the strip, as shown in Fig. 28-37. A potential difference of 2.99 µV is measured between points x and y across the strip. Calculate the speed v.


http://img521.imageshack.us/img521/4905/wirept9.gif


Ok i know Fnet= qE+q(V x B) and then set equal to zero cause equilibrium and get E=-q x V

(the x means cross product)

So now explain to me Why E=Vb in this case. Then i use V=E/B to get my speed velocity. But i don't just understand why the negative sign is dropped of ? Is it because its absolute value or cause Electric Field is point from a + to a - potential, in the x-axis direction ?

Thanks for your help

 

[alphysicist]

Hi th3plan,

Homework Statement

metal strip 6.66 cm long, 1.11 cm wide, and 0.837 mm thick moves with constant velocity through a uniform magnetic field B = 1.55 mT directed perpendicular to the strip, as shown in Fig. 28-37. A potential difference of 2.99 µV is measured between points x and y across the strip. Calculate the speed v.


http://img521.imageshack.us/img521/4905/wirept9.gif


Ok i know Fnet= qE+q(V x B) and then set equal to zero cause equilibrium and get E=-q x V

(the x means cross product)

So now explain to me Why E=Vb in this case. Then i use V=E/B to get my speed velocity. But i don't just understand why the negative sign is dropped of ? Is it because its absolute value or cause Electric Field is point from a + to a - potential, in the x-axis direction ?

The sign is different because the equations are two different things. The equation with the minus sign is a vector equation (it should be $\vec E = - \vec v\times\vec B$); the other equation is only dealing with the magnitudes.

For example, suppose I am holding a weight W by applying a force F upwards. The vector equation for equilibrium would be

$$\vec F = -\vec W$$
which means that my applied force is equal in magnitude and opposite in direction to the weight. If I wanted to calculate the magnitude of the force, I might write:

$$F = W$$
which just means $| \vec F | = | \vec W|$.

 

[baba89]

!

I would first like to clarify that the content provided is discussing the Crossfield Hall effect, which is a phenomenon in which a voltage is generated across a conductor moving through a magnetic field. This effect is used in devices such as Hall effect sensors and can be used to measure the speed of a moving conductor.

Now, to answer your question about why the negative sign is dropped off in the equation E=Vb, we need to understand the direction of the electric field and the direction of the magnetic field in this scenario. In this case, the electric field is directed from point x to point y, while the magnetic field is directed out of the page (perpendicular to the plane of the metal strip). The cross product of the electric field and the magnetic field gives us the direction of the force on the moving charges, which is in the opposite direction of the motion of the conductor.

Since the force is acting in the opposite direction of the motion, the negative sign is dropped off when calculating the speed using the equation V=E/B. This is because we are only interested in the magnitude of the velocity, not the direction. Therefore, the absolute value of the electric field can be used in this calculation.

In summary, the negative sign is dropped off because the force is acting in the opposite direction of the motion, and we are only interested in the magnitude of the velocity. I hope this explanation helps to clarify your understanding.