Electric field calculations
Physics-Electric field calculations
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S V Kumar W00949413 26 Jan 2010 Phys 368 Homework 3
(02.03): Let k = (40 ) . From diagram, with as the angle between the z axis and the electric field dE contributed by the charge element dq = dx:
-1
x2 + z 2 x sin = r z cos = r The x and y components of the electric field vector: r= dE
2
=k
dx r2
^ r
2
=k
dx r2
d Ex = d E d Ez = d E Thus, the total field at z is: d E = d E x + d Ez
L
2
sin x ^ cos z ^
2
(1)
L
3
=k = k = k
x dx + z2) 2 z2)
L
x=0 (x2
x+k ^
z dx
3
x=0 (x2 L
+ z2) 2 dx
z ^ z ^
L
1 2
(2) (3) z ^ (4) (5) (6)
x dx +
1 2 3 2
x=0 (x2
x + kz ^ x + kz ^
3
x=0 (x2
+ z2) 2
x=0 (x2 + z 2 ) z 2 (x2 + z 2 ) -1 -1 kL = k z ^ - x+ ^ 1 2 + z2 z 2 + z2) 2 L z(L 1 1 kL = k - x+ ^ z ^ 1 2 + z2 z L z(L2 + z 2 ) 2
-1
L
x
x=0
For z L, l2 + z 2 z 2 = z The x component vanishes, leaving only a contribution in the direction of z : ^
1
dE
kL k ...
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