# Magnetic field problem: What are the magnitude and direction of the electric field

## Homework Statement

I am confused about two parts of the question. 1 How are they getting the calculation of dB/dt=0.06 and how do they know the direction of the field is perpendicular to r and couterclockwise?

A magnetic field directed into the page changes with time according to B=(0.03t^2+1.4)T, where t is in seconds. The field has a circular cross section of radius R=2.5cm. What are the magnitude and direction of the electric field at point P1 when t=3.00s and r1=0.02m.

The figure is located on this webpage at the bottom: http://www.phys.ncyu.edu.tw/~ccliu/index.files/course2.files/Ch29to31Appl.pdf [Broken]

It's basically a circle. P2 is on the outside going toward the center. P1 is going up and to the right but is inside the circle. R in going down and right out of the circle.

## Homework Equations

I am confused about two parts of the question. 1 How are they getting the calculation of dB/dt=0.06 and how do they know the direction of the field is perpendicular to r and couterclockwise?

## The Attempt at a Solution

dB/dt=0.06t
E=(0.02m/2)(0.06)(3)(1) =1.8*10^-3 directed perpendicular to r1 and counterclockwise.

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1) Take the derivative of B with respect to time to get dB/dt.

2) You can derive the direction from Faraday's law. Or you can use the right hand rule, where you align your thumb in the direction opposite of the changing magnetic flux (in order to oppose the changing flux) and your fingers curl in the direction of the E-field.

In this case since area is fixed and the magnetic field is increasing into the page, you point your thumb out of the page and curl your fingers using your right hand.