Transcript Unit 1 Day 16: Electric Potential due to any Charge

Unit 1 Day 16: Electric Potential due to any
Charge Distribution
• Electric Field due to a single point charge
• Electric Potential of a ring of charge
• Electric Potential due to a charged disk
Electric Potential of a Single Point
Charge
• The electric potential due to a single point
charge is:
1 Q
V
4 0 r
• In a region where there is a distribution of
electric charge, we can sum over all the
individual point charges, relative to some point
a:
n
1 n Qi
Va  Vi 

4

i 1
0 i 1 ria
• If the charge distribution is continuous, then:
1
dq
V
4 0  r
Electric Potential of a Ring of Charge
• A thin circular ring which has a uniformly distributed
charge Q, the electric potential at point P on the axis of
the ring is:
1
dq
1
1
V


40 r 40 x 2  R 2

1
dq 

4 x

1
2
0
1 Q
• For x>>R, this result reduces to: V 
4 0 x
Q
2
R
2

1
2
Electric Potential due to a Charged
Disk
•
A thin, flat disk of radius R0, having
A uniformly distributed charge
•
Divide the disk into thin rings of
Radius R, and thickness dR, so we
Can use the previous result.
•
The disk is uniformly charged (Q),
So that the charge contained in each
Q
Ring is proportional to its area. V 
2
4

R
•
For x>>R0:
0 0
1 Q
V
4 0 x

 x R

2
2
0

1
2
 x
