Within the green dashed circle shown in the figure below, the magnetic field changes with time according to the expression B = 7.00t3 - 3.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.10 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 = 4.20 cm from the center of the circular field region.
(b) At what instant is this force equal to zero?
Within the green dashed circle shown in the figure below, the magnetic field changes with time according to the expression B =10.00t3 ? 1.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.05 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= 4.10 cm from the center of the circular field region.
(c) At what instant is this force equal to zero?
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) = - dphi/dt
dphi/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 = 10.00t3 ? 1.00t2 + 0.800
dB = 30t^2 - 2t, at time t=2, so
dB = 116
Plugging dB and A into the equation for E we get:
E = 116*(pi*R^2) /(2pi*r1)
R = 2.05 cm = 2.05*10^-2 m
r1 = 4.1 cm = 4.1*10^-2 m
so,
E = 116*(pi*(2.05*10^-2 m)^2) /(2pi*4.1*10^-2 m) = 29N/C
Now we can plug this back into the equation for Force,
Force = 29*(1.602*10^-19 C) = 46.45E-19 N
Using Right Hand Rule, we know this force is clockwise
Part C,
The force is equal to zero dB/dt = 0
dB = 30t^2 - 2t = 0
t = 1/15 s
Solving for t, we get t = 4/21 s
Within the green dashed circle shown in the figure below, the magnetic field changes with time...
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