(a) The time rate of increase of electric field between the plates can be calculated using the formula for the current I = dQ/dt, where Q is the charge and t is the time.

The charge on a capacitor is given by Q = CV, where C is the capacitance and V is the voltage. For a parallel plate capacitor, the capacitance is given by C = εA/d, where ε is the permittivity of free space, A is the area of one of the plates, and d is the separation between the plates.

The electric field E between the plates of a capacitor is given by E = V/d.

Substituting the expression for Q from the equation Q = CV into the equation for the current gives I = d(CV)/dt = C dV/dt.

Substituting the expression for E from the equation E = V/d into the equation for the current gives I = C d(E*d)/dt = C*dE.

Solving for dE/dt gives dE/dt = I/C.

Substituting the expression for C from the equation C = εA/d gives dE/dt = I/(εA/d) = Id/(εA).

The area of the plates can be calculated using the formula for the area of a circle, A = πr^2, where r is the radius of the plates.

Substituting this into the equation for dE/dt gives dE/dt = Id/(επr^2).

Substituting the given values gives dE/dt = (0.210 A)(0.00400 m)/[(8.85 x 10^-12 C^2/N*m^2)(π)(0.116 m)^2] = 2.02 V/(m·s).

(b) The magnetic field B between the plates can be calculated using Ampere's law, which states that the integral of B over a closed loop is equal to μI, where μ is the permeability of free space and I is the current.

For a circular loop of radius r, the integral of B over the loop is B*2πr, so B = μI/(2πr).

Substituting the given values gives B = (4π x 10^-7 T*m/A)(0.210 A)/(2π(0.0500 m)) = 2.64 x 10^-6 T.

The electric flux Φ through a circle of radius r lying parallel to the plates, midway between them, can be calculated using the formula Φ = EA, where E is the electric field and A is the area of the circle.

Substituting the given values gives Φ = (2.02 V/m)(π(0.0500 m)^2) = 0.159 N*m^2/C.

Question

(a) The time rate of increase of electric field between the plates can be calculated using the formula for the current I = dQ/dt, where Q is the charge and t is the time.

The charge on a capacitor is given by Q = CV, where C is the capacitance and V is the voltage. For a parallel plate capacitor, the capacitance is given by C = εA/d, where ε is the permittivity of free space, A is the area of one of the plates, and d is the separation between the plates.

The electric field E between the plates of a capacitor is given by E = V/d.

Substituting the expression for Q from the equation Q = CV into the equation for the current gives I = d(CV)/dt = C dV/dt.

Substituting the expression for E from the equation E = V/d into the equation for the current gives I = C d(E*d)/dt = C*dE.

Solving for dE/dt gives dE/dt = I/C.

Substituting the expression for C from the equation C = εA/d gives dE/dt = I/(εA/d) = Id/(εA).

The area of the plates can be calculated using the formula for the area of a circle, A = πr^2, where r is the radius of the plates.

Substituting this into the equation for dE/dt gives dE/dt = Id/(επr^2).

Substituting the given values gives dE/dt = (0.210 A)(0.00400 m)/[(8.85 x 10^-12 C^2/N*m^2)(π)(0.116 m)^2] = 2.02 V/(m·s).

(b) The magnetic field B between the plates can be calculated using Ampere's law, which states that the integral of B over a closed loop is equal to μI, where μ is the permeability of free space and I is the current.

For a circular loop of radius r, the integral of B over the loop is B*2πr, so B = μI/(2πr).

Substituting the given values gives B = (4π x 10^-7 T*m/A)(0.210 A)/(2π(0.0500 m)) = 2.64 x 10^-6 T.

The electric flux Φ through a circle of radius r lying parallel to the plates, midway between them, can be calculated using the formula Φ = EA, where E is the electric field and A is the area of the circle.

Substituting the given values gives Φ = (2.02 V/m)(π(0.0500 m)^2) = 0.159 N*m^2/C.

Knowee AI · Accepted Answer