Consider the situation shown in the figure below. An electric field of 300 V/m is confined to a circular area d = 10.4 cm in diameter and directed outward perpendicular to the plane of the figure. Consider that the field is increasing at a rate of 19.0 V/m · s.

+4 votes

Consider the situation shown in the figure below. An electric field of 300 V/m is confined to a circular area d = 10.4 cm in diameter and directed outward perpendicular to the plane of the figure. Consider that the field is increasing at a rate of 19.0V/m · s.

image
(a) What is the direction of the magnetic field at the point Pr = 14.7 cm from the center of the circle?
    

(b) What is the magnitude of the magnetic field at the point Pr = 14.7 cm from the center of the circle?
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asked Mar 27, 2012 in Physics by yoshi ~Expert~ (919 points)
    

1 Answer

+3 votes

Part A:  Use Right hand Rule, thumb pointing in direction of E, so your fingers would point "upwards" at p.

Part B:

Given:

Electric field = 300 V / m

diameter (d) = 10.4 cm

radius (r) = 14.7 cm

Change in electric field = 19 V/m*s

Use the following formula from Maxwell's equation:

 

Electric Flux = Surface integral of Electric field *change in Area  

Change in Electric Flux = Change in Electric field * Area

first calculate the Area,

Area =  pi*radius^2       , since radius = diameter / 2

Area = pi*(d/2)^2

plugging back in the area and the change in electric field you can find the change in electric flux.

To find the magnitude of the magnetic field at p,

Use this formula, which has been derived from Maxwell's equations:

furthermore, I is 0, so magnetic field, B, is equal to:

B *2*pi*r =     

   (*where r, is the r given in question)

So ,

B = / 2

Plugging in the constants in front we get:

B = (4pi*10^-7)*(8.854*10^-12)*change in electric flux / (2pi*r)

 

answered Mar 30, 2012 by Roar3215 ~Expert~ (1,318 points)
edited Mar 30, 2012 by Roar3215

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