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21.64:
a) The magnitude of the field the due to each charge is
,
)
)
2
(
1
4
4
1
2
2
0
2
0
+
=
=
x
d
πε
q
r
q
πε
E
where
d
is the distance between the two charges. The
x
-components of the forces due to
the two charges are equal and oppositely directed and so cancel each other. The two
fields have equal
y
-components, so:
θ
x
d
πε
q
E
E
y
sin
)
2
(
1
4
2
2
2
2
0
+
=
=
where
θ
is the angle below the
x
-axis for both fields.
;
)
2
(
2
sin
2
2

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**Unformatted text preview: **x d d θ + = thus 2 3 2 2 2 2 2 2 dipole ) ) 2 (( 4 ) 2 ( 2 ) 2 ( 1 4 2 x d πε qd x d d x d πε q E + = + + = The field is the y-directions. b) At large , ) 2 ( , 2 2 d x x so the relationship reduces to the approximations 3 dipole 4 x πε qd E ≈...

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