Magnetic Field Problem: Magnitude & Dir of Electric Field

In summary, the question involves a changing magnetic field with a circular cross section and a given equation. The magnitude and direction of the electric field at a specific point is being asked. To solve this, take the derivative of the magnetic field with respect to time and use Faraday's law or the right hand rule to determine the direction of the electric field.
  • #1
qwerty11
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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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  • #2


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.
 

What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is produced by moving electric charges and can be represented by lines of force that indicate the direction and strength of the field.

How is the magnitude of a magnetic field measured?

The magnitude of a magnetic field is typically measured in units of tesla (T) or gauss (G). One tesla is equal to 10,000 gauss. The strength of a magnetic field can also be measured with a magnetometer, which uses sensors to detect the strength of the field.

What is the direction of the electric field in a magnetic field?

The direction of the electric field in a magnetic field is always perpendicular to the direction of the magnetic field. This means that the electric field lines and magnetic field lines are always at right angles to each other.

How does the magnitude of the magnetic field affect the electric field?

The magnitude of the magnetic field can affect the electric field by inducing a force on electric charges. This force, known as the Lorentz force, causes charged particles to move in a circular or helical path in a magnetic field. The strength of the force is dependent on the magnitude of the magnetic field.

What is the direction of the magnetic field around a current-carrying wire?

The direction of the magnetic field around a current-carrying wire follows the right-hand rule. If you point your right thumb in the direction of the current flow, the direction of the magnetic field will be in the direction that your fingers curl around the wire.

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