Electric fields
Question:
1.
Calculate the electrostatic force between an alpha particle (charge = 2e) and a gold nucleus
(charge = 79e) when they are separated by 3.6x10
-14 m
2. Calculate the electric field
intensity at the following places:
(i) between a thunder cloud and the ground if the p.d.
between the cloud and the ground is 1000MV and the cloud is 1 km above it
(Relative
permittivity for air = 1.0000536.)
(ii) 4.5m from the dome of a Van de Graaff generator if
the charge on the dome is 2.5x10
-5 C.
3. Calculate the electrostatic force between
the proton and the electron in the hydrogen atom if the separation of the two particles is
1.0x10
-10 m
4. Two small equally charged are 10 cm apart and the repulsive force
between them is 3.6x10
-6 N
(i) what is the charge on each sphere?
(ii) the spheres
are negatively charged. How many excess electrons are there on each
sphere?
Answers
The formulae you will need are:
F =
[1/4πε
o]Q
1Q
2/d
2 E (radial field) =
[1/4πε
o]Q/d
2 and E (uniform field) = V/d
I am assuming that you have
been given the values of all the basic constants.
Remember that the charges must be in
coulombs and the distances in metres because of the value taken for the constant.
A
useful value that I will use is that 1/4πε
o = 9x10
9 using the correct units (see above) for
distance and charge.
1. Use: F =
[1/4πε
o]Q
1Q
2/d
2 F =
[1/4πε
o]Q
1Q
2/d
2
= [9x10
9x2x1.6x10
-19x79x1.6x10
-19]/(3.6x10
-14)
2 = 28.1 N
2.
(i) Use: E = V/d = 1.0000536x1000x10
6/1000 =
1.0000536x10
6 Vm
-1 = 1.0000536 MVm
-1(ii) Use: E (radial field) =
[1/4πε
o]Q/d
2 = 9x10
9x2.5x10
-5/4.5
2 = 1.11x10
4 Vm
-1 = 11 000 Vm
-1
3.
Use: F = [1/4πε
o]Q
1Q
2/d
2 F =
[1/4πε
o]Q
1Q
2/d
2
= [9x10
9x1.6x10
-19x1.6x10
-19]/(1.0x10
-10)
2 = 2.3x10
-8 N
4. Use: F =
[1/4πε
o]Q
1Q
2/d
2 but Q
1 = Q
2 = Q
(i) Therefore:
Q
2 = Fd
2/[1/4πε
o] = 3.6x10
-6x0.12/9x10
9 = 4x10
-18 C = 40x10
-19 C
(ii)
Number of electrons = Q/e = 40x10
-19 /1.6x10
-19 = 25 electrons
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