# When t = 2.00 s, calculate the magnitude of the force exerted on an electron located at point P1, which is at a distance r1 = 5.70 cm from the center of the circular field region.

Within the green dashed circle shown in the figure below, the magnetic field changes with time according to the expression B = 7.00t3 − 2.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.85 cm.

(a) When t = 2.00 s, calculate the magnitude of the force exerted on an electron located at point P1, which is at a distance r1 = 5.70 cm from the center of the circular field region.
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(b) When t = 2.00 s, calculate the direction of the force exerted on an electron located at point P1, which is at a distance r1 = 5.70 cm from the center of the circular field region.

(c) At what instant is this force equal to zero?
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asked Feb 28, 2012 in Physics
edited Mar 3, 2012

Force = E*q     (*where E=electric field, q=charge (of electron) = 1.602*10^-19 C )

To find force, first find E.

Emf = integral( E*ds) =  - dΦB/dt

B/dt = B*A   (*where A=area)

A = (pi*R^2)

So, we can now solve for E, by taking the derivative of Emf:

integral( E*ds) = B*A       becomes...

E = dB*A/ds

**note ds = 2pi*r1

We find dB by taking the derivative of B:

B = 7.00t3 − 2.00t2 + 0.800,

dB = 21t2 - 4t, at time t=2, so

dB = 76

Plugging dB and A into the equation for E we get:

E = 76*(pi*R^2) /(2pi*r1)

R = 2.85 cm = 2.85*10^-2 m

r1 = 5.7 cm = 5.7*10^-2 m

so,

E = 76*(pi*(2.85*10^-2 m)^2) /(2pi*5.7*10^-2 m)

Now we can plug this back into the equation for Force,

Force = (76*(pi*(2.85*10^-2 m)^2) /(2pi*5.7*10^-2 m)  )*(1.602*10^-19 C)

Using Right Hand Rule, we know this force is clockwise

Part C,
The force is equal to zero dB/dt = 0
dB = 21t- 4t = 0

Solving for t, we get t = 4/21 s
answered Mar 7, 2012 by ~Expert~ (3,856 points)
edited Apr 19, 2012
why is the A=pi*R^2/2pir1
Thanks for catching this, The 2pi*r is actually the ds part of (E*ds), I had divided it over to the other side of the equation combined it with the A term, I have edited the answer to make it more clear.

+1 vote