Electric Potential
THE WORK DONE BY A CONSERVATIVE
FORCE ALWAYS HAS FOUR PROPERTIES:
1.
It can be expressed as the difference between the initial and final values of a potential-energy function.
3.
It is independent of the path of the body and depends only on the starting and ending points.
2.
It is reversible.
4.
When the starting and ending points are the same, the total work is zero.
The total mechanical energy ME = K + U is constant.
Object moving in a uniform gravitational field
gravitational
a
U = Fh = mgh d ha
F=mg
Wab = Fd
= ‒ ΔU = ‒ (Ub ‒ Ua)
b
hb
direction of gravitational field
F does positive work,
U decreases
positive charge moving in the direction of uniform E
+
+
+
+
+
+ electric U = Fy = q0Ey
a
F=Eq0
E
Wab = Fd = q0Ed d b
ya yb ‒
‒
‒
‒
‒
‒
= ‒ ΔU = ‒ (Ub ‒ Ua)
F does positive work,
U decreases
positive charge moving in the opposite direction of uniform E
+
+
+
+
+
+ electric U = Fy = q0Ey
b
Wab = Fd = q0Ed
d
E
yb a ya
F=Eq0
‒
‒
‒
‒
= ‒ ΔU = ‒ (Ub ‒ Ua)
‒
‒
F does negative work,
U increases
negative charge moving in the direction of uniform E
+
+
+
+
+
+ electric F=Eq0
U = Fy = q0Ey
a
Wab = Fd = q0Ed
E
= ‒ ΔU = ‒ (Ub ‒ Ua)
d ya b yb ‒
‒
‒
‒
‒
‒
F does negative work,
U increases
negative charge moving in the opposite direction of uniform E
+
+
+
+
+
+ electric U = Fy = q0Ey b E
Wab = Fd = q0Ed
F=Eq0
d yb = ‒ ΔU = ‒ (Ub ‒ Ua)
a ya ‒
‒
‒
‒
‒
‒
F does positive work,
U decreases
charge qo moving through non-uniform E b a
F=Eq0
E
charge qo moving through non-uniform E b a
charge qo moving through non-uniform E b a
charge qo moving through non-uniform E b a
Potential energy is always defined relative to some reference point where U=0.
U is zero when q and q0 are infinitely far apart and r = .
Therefore, U represents the work that would be done on the test charge q0 by the field of q if q0 moved from an initial distance r to infinity.
If
FORCE ALWAYS HAS FOUR PROPERTIES:
1.
It can be expressed as the difference between the initial and final values of a potential-energy function.
3.
It is independent of the path of the body and depends only on the starting and ending points.
2.
It is reversible.
4.
When the starting and ending points are the same, the total work is zero.
The total mechanical energy ME = K + U is constant.
Object moving in a uniform gravitational field
gravitational
a
U = Fh = mgh d ha
F=mg
Wab = Fd
= ‒ ΔU = ‒ (Ub ‒ Ua)
b
hb
direction of gravitational field
F does positive work,
U decreases
positive charge moving in the direction of uniform E
+
+
+
+
+
+ electric U = Fy = q0Ey
a
F=Eq0
E
Wab = Fd = q0Ed d b
ya yb ‒
‒
‒
‒
‒
‒
= ‒ ΔU = ‒ (Ub ‒ Ua)
F does positive work,
U decreases
positive charge moving in the opposite direction of uniform E
+
+
+
+
+
+ electric U = Fy = q0Ey
b
Wab = Fd = q0Ed
d
E
yb a ya
F=Eq0
‒
‒
‒
‒
= ‒ ΔU = ‒ (Ub ‒ Ua)
‒
‒
F does negative work,
U increases
negative charge moving in the direction of uniform E
+
+
+
+
+
+ electric F=Eq0
U = Fy = q0Ey
a
Wab = Fd = q0Ed
E
= ‒ ΔU = ‒ (Ub ‒ Ua)
d ya b yb ‒
‒
‒
‒
‒
‒
F does negative work,
U increases
negative charge moving in the opposite direction of uniform E
+
+
+
+
+
+ electric U = Fy = q0Ey b E
Wab = Fd = q0Ed
F=Eq0
d yb = ‒ ΔU = ‒ (Ub ‒ Ua)
a ya ‒
‒
‒
‒
‒
‒
F does positive work,
U decreases
charge qo moving through non-uniform E b a
F=Eq0
E
charge qo moving through non-uniform E b a
charge qo moving through non-uniform E b a
charge qo moving through non-uniform E b a
Potential energy is always defined relative to some reference point where U=0.
U is zero when q and q0 are infinitely far apart and r = .
Therefore, U represents the work that would be done on the test charge q0 by the field of q if q0 moved from an initial distance r to infinity.
If