Question

A 1200-nF capacitor with circular parallel plates 2.0 cm in diameter is accumulating charge at the rate of 35 mC/s at some instant in time. (A) What will be the magnitude of the induced magnetic field 10.0 cm radially outward from the center of the plates?

Answer 1

The magnitude of the induced magnetic field at a distance of 10.0 cm radially outward from the center of the plates can be calculated using Ampere's Law. It is given by B = μ₀(I/C), where I is the rate of change of charge and C is the circumference of the circular loop at that distance. Substituting the given values, we can calculate the magnitude of the induced magnetic field.

Step-by-step explanation:

The magnitude of the induced magnetic field at a distance of 10.0 cm radially outward from the center of the plates can be calculated using Ampere's Law. Ampere's Law states that the magnetic field around a closed loop is equal to the sum of the products of the current enclosed by the loop and the permeability of free space. In this case, the induced magnetic field can be obtained by dividing the rate of change of charge with time by the circumference of the circular loop at a radial distance of 10.0 cm from the center of the plates.

Given that the rate of change of charge is 35 mC/s and the radius of the circular loop is 10.0 cm, we can calculate the circumference of the loop using the formula C = 2πr. Substituting the values, we get C = 2π(10.0 cm) = 20π cm.

Now, we can calculate the magnitude of the induced magnetic field B using the formula B = μ₀(I/C), where I is the rate of change of charge and C is the circumference of the loop. Substituting the values, we get B = μ₀(35 mC/s)/(20π cm).