Electric field calculations
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Transcript Electric field calculations
Electric field calculations
We practice how to calculate the electric field created by charge
distributed over space
Basic idea: apply the superposition principle of electric field
We go from the fundamental principle E(r)= E1(r) + E2(r)
to fully exploit E ( r ) E 1 ( r ) E 2 ( r ) E 3 ( r ) ...
Electric field on the axis of a ring of charge
homogeneously
charged ring
Total charge Q
Radius a
Q
Line charge density
r
x a
2
2
co n st .
P
dEx
2 a
dEy
Q
E ( x , y 0) e x dE x
with
dE x
cos dQ
4 0 r
2
x
dQ
4 0 r
3
E ( x, y 0) e x
0
x
dQ
x
4 0 r
Q
4 r
3
ex
3
Brief discussion of limiting case x>>a
r
x a
2
2
co n st .
r
Ring structure becomes less “visible” from distant point P
E-field of a point charge
E
x
Q
4 0 r
3
ex
x
4 0
Q
x
2
a
2
3/2
ex
x
Q
4 0 x
x>>a
3
ex
1
Q
4 0 x
2
ex
x a
2
2
x
Electric field on the axis of uniformly charged plate
homogeneous charge per plate area
Q
R
2
We consider the plate as a collection of rings
x
we take advantage of our ring solution E
4 0
Q
x
2
a
2
3/2
ex
da
a
Every ring of radius 0<a<R contributes with dQ 2 ada
R
E ex
0
2 ada
x
4 0
x
2
a
2
ex
3/2
x
R
2 0
0
2
E ex
x
2 0
2
x R
x
ada
x
x R
2
dz
z
2
2
a
2
3/2
2
x 1
ex
2 0 x
x 1
ex
2 0 z
x
with
z x a zdz ada
2
2
2
1
ex
2
2
2
x R
0
1
1
R / x
2
1
Brief discussion of limiting case R
E ex
1
2 0
1
R / x
2
1
ex
2 0
result independent of x
R
E
2 0
E
field direction everywhere perpendicular to the sheet
homogeneous field
2 0
we use this limiting case to derive
the electric field of two oppositely charged infinite sheets
sheet 2
E=0
above sheet2
E2
E=/0
E1
between the sheets
E2
E1
sheet 1
E2
E1
E=0
below sheet1
Demonstration
For a nice intuitive approach to an understanding of the Wimshurst machine watch also
MIT Physics Demo -- The Wimshurst Machine
http://www.youtube.com/watch?v=Zilvl9tS0Og