Voltage Induced in Coil: Hall Effect

[zooropa]

Homework Statement

[STRIKE][STRIKE][/STRIKE][/STRIKE]

http://img697.imageshack.us/img697/2317/img11l.jpg

(a = 0.10 m and b = 0.16 m)

i=3t^3 - 5t

(i - ampéres t - seconds)

Determine the voltage induced in the coil to the instant t = 3 sec. well as the current direction.

Homework Equations

Hall efect

The Attempt at a Solution

A= 0.016 m^2
For t= 3 sec ... i=3*3^3 - 5*3 ...i= 66 ampéres

 

[ideasrule]

V=-d(phi)/dt, so first find an equation for phi in terms of i. Deriving that equation with respect to time will get you d(phi)/dt.

 

[kerimek]

The voltage induced in the coil can be calculated using the formula V = B*l*v, where B is the magnetic field strength, l is the length of the coil, and v is the velocity of the charged particles in the coil. In this case, the velocity of the charged particles is equal to the current, i, divided by the cross-sectional area of the coil, A. Therefore, the voltage induced in the coil at t = 3 sec can be calculated as follows:

V = B*l*(i/A)

Since the magnetic field is perpendicular to the direction of current flow, the direction of the induced voltage will be determined by the right-hand rule. The direction of the induced voltage will be perpendicular to both the magnetic field and the direction of current flow.

Using the values given in the problem, we can calculate the voltage induced in the coil at t = 3 sec:

V = B*l*(i/A) = (0.10 m)*(0.16 m)*(66 A)/(0.016 m^2) = 660 V

Therefore, the voltage induced in the coil at t = 3 sec is 660 volts and the direction of the induced voltage will be perpendicular to both the magnetic field and the direction of current flow.