Within the green dashed circle shown in the figure below, the magnetic field cha
ID: 1289905 • Letter: W
Question
Within the green dashed circle shown in the figure below, the magnetic field changes with time according to the expression B = 9.00t3 ? 2.00t2 + 0.800, where B is in teslas, tis in seconds, and R = 2.30 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 = 4.60 cm from the center of the circular field region.
=____N
(c) At what instant is this force equal to zero?
=_____s
Explanation / Answer
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) = - d?B/dt
d?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 = 21t2 - 4t = 0
Solving for t, we get t = 4/21 s
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