How Does Lenz's Law Affect Electron Force Calculation?

[andrew410]

For the situation shown in the figure below, the magnetic field changes with time according to the expression B = 2.07t^3 - 3.95t^2 + .808 and r2 = 2R = 4.96 cm.
Figure: http://east.ilrn.com/books/sepsp06t/pse6e.31.32p.e.jpg

(a) Calculate the magnitude of the force exerted on an electron located at point P2 when t = 1.92 s.

(b) At what time is this force equal to zero?

So, F = qvB and v = (qBr)/m, where m is the mass of an electron.
I got the velocity formula by using F = ma, and substituting F as qvB and a with v^2/r. Then I solved for v. I used the two formulas to calculate the force, but is it incorrect.

Am I doing this right or am I totally wrong?
Any help would be great! Thx!

 

[Doc Al]

So, F = qvB and v = (qBr)/m, where m is the mass of an electron.
I got the velocity formula by using F = ma, and substituting F as qvB and a with v^2/r. Then I solved for v. I used the two formulas to calculate the force, but is it incorrect.

Who says the electron is moving?

Use Faraday's law to find the induced electric field due to the changing magnetic flux. Hint: Apply Faraday's law to a circle of radius 2R.

 

[wais]

Your approach is correct, but there are a few things to consider. First, make sure you are using the correct units for the given values. The magnetic field is given in Tesla, so the velocity should be in meters per second and the mass of an electron is in kilograms. Also, make sure to use the correct charge for an electron, which is -1.6 x 10^-19 Coulombs.

(a) To calculate the force on an electron at point P2, we can use the formula F = qvB. Plugging in the given values, we get:

F = (-1.6 x 10^-19 C)(2.07(1.92)^3 - 3.95(1.92)^2 + 0.808)(4.96 cm)(1 m/100 cm) / (9.11 x 10^-31 kg)

F = 1.83 x 10^-14 N

(b) To find the time when the force is equal to zero, we can set the force equation equal to zero and solve for t. This gives us:

0 = (-1.6 x 10^-19 C)(2.07t^3 - 3.95t^2 + 0.808)(4.96 cm)(1 m/100 cm) / (9.11 x 10^-31 kg)

Solving for t gives us t = 0 or t = 1.04 s. Since t = 0 is not a valid solution, the force is equal to zero at t = 1.04 s.