ORANGE COUNTRY
GO COWBOYS
PHYS2114
LECTURE 6
Instructor: Professor Donna Bandy
ORANGE COUNTRY
GO COWBOYS
CALCULATE the electric field from the electrical potential difference (or just ‘potential’) (in
general).
1
ORANGE COUNTRY
GO COWBOYS
PHYS2114
LECTURE 6
Instructor: Professor Donna Bandy
ORANGE COUNTRY
GO COWBOYS
Problem: Over a certain region of space, the electric potential is 𝑉 = 5𝑥 − 3𝑥 2 𝑦+2𝑦𝑧 2 . Find
the expression for the x, y, and z components of the electric field over this region and calculate
the magnitude of the field at the point P that has coordinates (1, 0, -2) m.
2
ORANGE COUNTRY
GO COWBOYS
PHYS2114
ORANGE COUNTRY
GO COWBOYS
LECTURE 6
Instructor: Professor Donna Bandy
Electrical potential Due to Continuous Charge Distributions:
Electric Potential Due to a Dipole ON AXIS: A dipole is two equal charges that are opposite in sign.
Electrical potential and Electric Field Due to a Uniformly Charged Ring
V ( x ) ring 
k eQ
x2  R2
R = a The radius of the ring on Eq. Sheet
3
ORANGE COUNTRY
GO COWBOYS
PHYS2114
ORANGE COUNTRY
GO COWBOYS
LECTURE 6
Instructor: Professor Donna Bandy
Electrical potential and Electric Field Due to a Uniformly Charged Disk
V ( x ) disk  2k e  x 2  R 2  x 


R is radius of the disk.
Electrical potential Due to a Finite Line of Uniform Charge
𝑄
ℓ+√𝑎2 +ℓ2
𝑉 = 𝑘𝑒 ℓ ln⁡[
⁡𝑎
]
a is perpendicular distance from finite line
4
ORANGE COUNTRY
GO COWBOYS
PHYS2114
LECTURE 6
Instructor: Professor Donna Bandy
ORANGE COUNTRY
GO COWBOYS
Problem: Calculate the work that must be done on charges brought from infinity to charge a
spherical shell of radius R = 0.100 m to a total charge Q = 125 C.
5
ORANGE COUNTRY
GO COWBOYS
PHYS2114
LECTURE 6
Instructor: Professor Donna Bandy
ORANGE COUNTRY
GO COWBOYS
Problem: A thin, uniformly charged rod has a linear uniform charge density . Find an
expression for the electric potential at P.
6