Electrostatics - Electric Field Intensity due to a Point Charge at Rest
1 Answer
Electric Field Intensity, often simply called Electric Field, is a fundamental concept in electrostatics. It's a vector field that describes the force experienced by a positive test charge placed at a certain point in space due to the presence of other charges. Let's discuss the electric field intensity due to a point charge at rest.
Consider a point charge
Q located at the origin (
0
,
0
,
0
0,0,0) in a three-dimensional Cartesian coordinate system. The electric field intensity (
E) at a point
(
,
,
)
(x,y,z) in space due to this point charge is given by Coulomb's Law:
=
⋅
2
E=
r
2
k⋅Q
Where:
E is the electric field intensity at the given point.
k is Coulomb's constant (
≈
8.9875
×
1
0
9
N m
2
/
C
2
k≈8.9875×10
9
N m
2
/C
2
in SI units).
Q is the magnitude of the point charge that is creating the electric field.
r is the distance between the point charge and the point where the electric field is being calculated.
Importantly, electric field is a vector quantity, meaning it has both magnitude and direction. The direction of the electric field at a point is radially outward from the point charge if it's positive, and radially inward if it's negative.
To find the electric field vector (
⃗
E
) at a point
(
,
,
)
(x,y,z), you can break down the formula into its vector components. Since the electric field is radially symmetric around the point charge, the electric field vector will have components only along the radial direction. The vector components would be:
=
⋅
⋅
3
E
x
=
r
3
k⋅Q⋅x
=
⋅
⋅
3
E
y
=
r
3
k⋅Q⋅y
=
⋅
⋅
3
E
z
=
r
3
k⋅Q⋅z
Where
r is the distance from the charge to the point
(
,
,
)
(x,y,z):
=
2
+
2
+
2
r=
x
2
+y
2
+z
2
This expression gives you the electric field at any point in space due to a point charge at rest.
Remember that electric field intensity is a vector field, so it's important to take into account both the magnitude and direction when working with it. Also, if you have multiple point charges, you can superpose the electric fields created by each charge to find the total electric field at a point.
Consider a point charge
Q located at the origin (
0
,
0
,
0
0,0,0) in a three-dimensional Cartesian coordinate system. The electric field intensity (
E) at a point
(
,
,
)
(x,y,z) in space due to this point charge is given by Coulomb's Law:
=
⋅
2
E=
r
2
k⋅Q
Where:
E is the electric field intensity at the given point.
k is Coulomb's constant (
≈
8.9875
×
1
0
9
N m
2
/
C
2
k≈8.9875×10
9
N m
2
/C
2
in SI units).
Q is the magnitude of the point charge that is creating the electric field.
r is the distance between the point charge and the point where the electric field is being calculated.
Importantly, electric field is a vector quantity, meaning it has both magnitude and direction. The direction of the electric field at a point is radially outward from the point charge if it's positive, and radially inward if it's negative.
To find the electric field vector (
⃗
E
) at a point
(
,
,
)
(x,y,z), you can break down the formula into its vector components. Since the electric field is radially symmetric around the point charge, the electric field vector will have components only along the radial direction. The vector components would be:
=
⋅
⋅
3
E
x
=
r
3
k⋅Q⋅x
=
⋅
⋅
3
E
y
=
r
3
k⋅Q⋅y
=
⋅
⋅
3
E
z
=
r
3
k⋅Q⋅z
Where
r is the distance from the charge to the point
(
,
,
)
(x,y,z):
=
2
+
2
+
2
r=
x
2
+y
2
+z
2
This expression gives you the electric field at any point in space due to a point charge at rest.
Remember that electric field intensity is a vector field, so it's important to take into account both the magnitude and direction when working with it. Also, if you have multiple point charges, you can superpose the electric fields created by each charge to find the total electric field at a point.