a current of 10A flows into a parallel plate capacitor with square plates with area .5m^2
how do you find the dE/dt between the plates?
what is the line integral B.dl around a circular closed contour with a diameter of 10cm perpendicular to the electric field?
The capacitance C of that capacitor is
C = epsilon*A/d
Also, the charge on the plates is
Q = CV
dQ/dt = I = C dV/dt = (C*d)dE/dt
= epsilon*A*dE/dt
where epsilon is the permittivity of the speace between the plates. d, the dap between the plates, cancels out. Solve for dE/dt.
Use Ampere's law to answer your second question. The line integral of B is proportional to the current I through the loop and a permeability constant, mu
To find the rate of change of electric field between the plates (dE/dt), you need to know the current flowing into the capacitor and the area of the plates. The formula to calculate dE/dt is given by:
dE/dt = I / (ε0 * A)
where:
- dE/dt is the rate of change of electric field between the plates,
- I is the current flowing into the capacitor, and
- A is the area of the plates.
In this case, the given current is 10A and the area of the plates is 0.5m^2. Plugging these values into the formula:
dE/dt = 10A / (ε0 * 0.5m^2)
The value of ε0 (epsilon naught) is the permittivity of free space, which is approximately 8.854 x 10^-12 F/m. Substituting this value:
dE/dt = 10A / (8.854 x 10^-12 F/m * 0.5m^2)
Now you can calculate the numerical value by dividing the current by the product of the permittivity of free space and the area.
Regarding the line integral B.dl around a circular closed contour perpendicular to the electric field, it seems like you are referring to Ampere's Law. Ampere's Law states that the line integral of the magnetic field (B) dotted with the differential length vector (dl) around a closed loop is equal to the product of the permeability of free space (μ0) and the total current passing through the loop (I_enc). The formula is given as:
∮ B.dl = μ0 * I_enc
In your case, the circular closed contour has a diameter of 10cm, which means the radius is 5cm or 0.05m. Since the diameter is perpendicular to the electric field, it suggests that the electric field does not contribute to the line integral. Therefore, the value of ∮ B.dl around this contour would be zero.