Charge is uniformly distributed around a ring of radius R = 2.40 cm, and the resulting electric field magnitude E
is measured along the ring’s central axis (perpendicular to the plane of the ring). At what distance from the
ring’s center is E maximum?
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Answer:
We find the maximum by differentiating equation and setting the result equal to zero.
dz
d
(
4πε
0
(z
2
+R
2
)
3/2
qz
)=
4πε
0
q
4πε
0
(z
2
+R
2
)
5/2
R
2
−2z
2
=0
which leads to z=R/
2
.
With R=2.40 cm,
we have z=1.70 cm.
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