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R - Galileo and Einstein

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Field on Axis from Two Opposite Charges<br />

• This is a dipole: the analysis is just like the two equal charges case:<br />

y-axis<br />

x-axis<br />

Q<br />

d<br />

d<br />

-Q<br />

R<br />

r<br />

<br />

P<br />

<br />

E<br />

kQrˆ<br />

<br />

r<br />

E<br />

upper charge 2<br />

total<br />

• Anywhere on the axis, the field is downward, <strong>and</strong> has value<br />

E<br />

2kQ 2kQd 2kQd 2kQd<br />

sin<br />

<br />

r 2 r 3 R<br />

R<br />

3<br />

<br />

2 2<br />

R d 3/2

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