A charge in the circular plates capacitor with radius of plates 5.0 cm depends on time as Q=1.0+5.00t^2-3.0t, where constants have units of C; C/s ^2 and C/s. At what distance from a center inside capacitor induced magnetic field at t= 1 s is equal to magnetic field outside 7.0 cm from the edge? Give answer in cm.

Distance (d) = 2.08 cm

Explanation:

From the given information:

A diagrammatic illustration is sketched and the image is attached below:

Suppose 'i' be the total current at any instant.

Then:

where Q = 1.0 +5.00t² - 3.0 t

i = 10.00t - 3.0

At t = 1s

i = 10.00(1) - 3.0

i = 7.00 amperes

Since the current at P is situated in the outside, the magnetic field B can be computed as:

Taking the ampere loop with radius (d) into consideration:

The current through the loop can be expressed as:

Thus; the magnetic field at P' i.e. the inside point is :

From the question; Since

Then:

d = 0.0208

d = 2.08 cm