Physics 7B
Answers for E3 (rev. 3.0)
Page 1
E3. Gauss’s Law
Questions for discussion
1.
Using what you know about the electric field, write down some rules for electric field lines.
•
Electric field lines can only
start
(
end
) at
positive
(
negative
) charges, or at infinity.
•
Electric field lines
can’t cross
.
•
The number of electric field lines coming out of a charge is proportional to the charge.
2
. Consider a pair of point charges ±Q, fixed in place near one another as shown.
a)
On the diagram above, sketch the field created by these two point charges.
b)
Now consider an imaginary spherical surface enclosing the +Q charge:
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Answers for E3 (rev. 3.0)
Page 2
i)
Reproduce here your drawing of the electric field lines from part (a), so you can get a sense of
how the field lines pierce the imaginary spherical surface.
ii)
How much electric flux passes outward through the imaginary spherical surface? You should
be able to arrive at the answer very quickly using Gauss’s Law.
The imaginary sphere contains a net charge +Q. So according to Gauss's Law, the net flux
passing outward through the sphere is
Φ
E
= +Q/
ε
0
.
iii)
By examining the field lines and how they pierce the imaginary spherical surface, try to
explain
why
the flux turns out to be what Gauss’s Law said it was. (For example, try to
explain why the net flux through the surface is
outward
.)
There are plenty of field lines passing both in and out through the surface. But in the region
where field lines are going out, the field is stronger. So the net flux is outward. The usual
convention in drawing field lines is that the field lines are more closely spaced where the field
is most intense.
Provided we adhere to this convention in our drawing
, then it suffices simply
to count the number of field lines going in and going out.
c)
Next, consider an imaginary
ellipsoidal
surface enclosing both charges:
i)
Once again, reproduce your drawing of the electric field lines from part (a), so you can get a
sense of how the field lines pierce the imaginary ellipsoidal surface.
ii)
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 Fall '10
 yildiz
 Physics, Electrostatics, Magnetic Field, Electric charge, field lines

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