What is the
nature of this potential? In the electric potential at a distance r from a point charge q.
Answers
Answer:
Consider the electric potential due to a point charge q, As we move from point A, at distance rA from the charge q, to point B, at distance rB from the charge q, the change in electric potential is
ΔV
BA
=V
B
−V
A
=−∫
A
B
E.ds
E.ds=[k
r
2
q
]
r
^
.ds
r
^
.ds=dr
Only the radial distance r determines the work done or the potential. We can move through any angle we like and, as long as the radial distance remains constant, no work is done or there is no change in the electric potential.
ΔV
BA
=V
B
−V
A
=−∫
r
A
r
B
Edr=−∫
r
A
r
B
[k
r
2
q
dr]
ΔV
BA
=V
B
−V
A
=−kq[(−1)r
−1
]
r
A
r
B
ΔV
BA
=V
B
−V
A
=kq[
r
B
1
−
r
B
1
]
Explanation:
Using calculus to find the work needed to move a test charge q from a large distance away to a distance of r from a point charge Q, and noting the connection between work and potential (W = −qΔV), it can be shown that the electric potential V of a point charge is V=kQr V = k Q r (Point Charge), where k is a constant ...