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Lesson 2.5 Homework Solutions
1.
In the Bohr model of the hydrogen atom, the electron orbit closest to the nucleus
has a radius of 5.29
×
10
11
m. (i) Find the electric potential of the proton at the
position of the electron. (ii) Calculate the electric potential energy of the electron
at this position.
9
9
11
1
19
1
9 10
1.602 10
27.3
5.
4.4 10
29 10
2.73 1.602 10
kq
V
V
U
J
r
Vdq




×
×
×
=
=
=
×
∆
= 

×
= 
×
×
=
2.
A uniform electric field of 2 kN.C
1
is in the x direction. A positive charge q = 3
μ
C is released from rest at the origin. (i) What is the potential difference V(4 m) –
V(0)?. (ii) What is the change in potential energy of the charge from x = 0 to x =
4 m? (iii) What is the kinetic energy of the charge when it is at x = 4 m. (iv) find
the potential V(x) if (a) V(0) = 0, (b) V(1) = 0.
(i)
∆
v =  E
∆
x =  2.0
×
10
3
×
4
=
 8.0 kV
(ii)
The change in potential energy
∆
U is a measure of the work
done on the charge.
Work done = Charge
×
potential difference.
∆
U = q
∆
V = 3
×
10
6
×
(8
×
10
3
)
=
24 mJ.
(iii)
Loss in potential energy = gain in kinetic energy
K
=
24 mJ
(iv)
(a)
(2000
)
2000
V
Edx
d
x
c
x
= 

=
=
+

∫
∫
(b)
V(0) = 0 gives c = 0
V(x) = 2000x
(c)
V(1) = 0 gives 0 = 2000 + c, or c = 2000
V = (2000x – 2000) =
2000 – 2000x
3.
A constant electric field E = 5.6
×
10
3
N.C
1
i
exists in a region of space. What is
the potential difference between the initial point x = 0 and the final point x = 5m?
∆
V =  E
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 Spring '11
 George
 Physics, Electric Potential, Work

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