Question

Consider the situation shown below in which you have two plates of radius R = 1.25 cm which have between them an electric field given by一4t V/m. The electric field is 0 everywhere except between those plates. You are interested in calculating the magnetic field a distance r 9.5 cm away from the midpoint between the plates We'll walk through the various pieces of Ampere's Law through the course of the problem. a. What is the enclosed current within the loop? enc b. What is the change in electric flux passing through the loop? Vin d't dt c. What is the expression for B df around the loop? You can assume that the magnetic field B is constant along the loop. This is just an expression, so variables only. d. Pulling it all together, what is the magnitude of the magnetic field a distance r from the center? This should be a number e. Is this field pointing clockwise or counterclockwise when viewed from above? Justify your answer.

Answer 1

Solution

a) To determined the current that through the loops. We use the Gauss Law already of the two plates

$\oint \vec{E}\cdot d\vec{s}=\frac{q}{\varepsilon _{0}}$

e0

In this case the electric field vector and the loops surface are parallel

$-4t\oint 2\pi rdr=\frac{q}{\varepsilon _{0}}$

E0

Clearing q

$q=-4t\pi r^{2}\varepsilon _{0}$

Now the current of the loops is calculated as follows

dq dt

ー4mr2

=-4m * (9.5X10-2) 2 * (8.85x10-12)

íー-1.003110-12A

Now