Download IB Physics Review -Electrostatics and Fields

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IB PHYSICS HL
REVIEW PACKET: ELECTROSTATICS AND FIELDS
1.
This question is about forces on charged particles in electric and magnetic fields.
The diagram shows two parallel plates situated in a vacuum. One plate is at a positive potential with respect to the other.
+
Path of positively charged particle
–
A positively charged particle passes into the region between the plates. Initially, the particle is travelling parallel to the plates.
(a)
On the diagram,
(i)
draw lines to represent the electric field between the plates.
(3)
(ii)
show the path of the charged particle as it passes between, and beyond, the plates.
(2)
(b)
An electron is accelerated from rest in a vacuum through a potential difference of 750 V.
(i)
Determine the change in electric potential energy of the electron.
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(2)
(ii)
7
–1
Deduce that the final speed of the electron is 1.6 × 10 m s .
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(2)
1
2.
This question is about forces on charged particles.
(a)
A charged particle is situated in a field of force. Deduce the nature of the force-field (magnetic, electric or gravitational)
when the force on the particle
(i)
is along the direction of the field regardless of its charge and velocity;
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(ii)
is independent of the velocity of the particle but depends on its charge;
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(iii)
depends on the velocity of the particle and its charge.
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(5)
(b)
An electron is accelerated from rest in a vacuum through a potential difference of 2.1 kV. Deduce that the final speed of
7
–1
the electron is 2.7 × 10 m s .
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(3)
The electron in (b) then enters a region of uniform electric field between two conducting horizontal metal plates as
shown below.
+95 V
Path of
electron
P
2.2 cm
2.7 × 107 m s–1
0V
12 cm
The electric field outside the region of the plates may be assumed to be zero. The potential difference between the plates is 95 V
and their separation is 2.2 cm.
As the electron enters the region of the electric field, it is travelling parallel to the plates.
(c)
(i)
(ii)
On the diagram above, draw an arrow at P to show the direction of the force due to the electric field acting on the
electron.
(1)
Calculate the force on the electron due to the electric field.
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(3)
2
3.
This question is about the physics of a lightning strike.
In a simple model of a thundercloud, a negative charge is built up on the base of the cloud by the process of charge separation.
The resulting electric field between the cloud and the ground is approximately the same as that between two infinite parallel
charged plates. When the charge on the base of the cloud reaches a certain value, a lightning strike occurs between the ground
and the base of the cloud.
thundercloud
500 m
ground
(a)
Explain what is meant by the term charge separation.
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(2)
(b)
Define electric field strength.
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(2)
(c)
On the above diagram, draw the electric field pattern between the ground and the base of the cloud.
(3)
The electric field strength E between two infinite, parallel charged plates is given by
E=

0
2
where σ is the charge on an area of 1 m of one plate.
Just before a lightning strike, a particular thundercloud carries a charge of 20 C spread over its base. The area of the base of the
6 2
cloud is 7 × 10 m .
3
(d)
(i)
Show that the magnitude of the electric field between the base of the cloud and the ground is approximately 3 ×
5
–1
10 Vm .
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(3)
(ii)
State two assumptions made when applying this formula.
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(2)
(e)
The base of the cloud is at an average height of 500 m. Calculate the potential difference between the ground and the
cloud base just before the lightning strike.
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(2)
When a lightning strike occurs between the ground and the base of this thundercloud, the cloud completely discharges in a time
of 20 ms.
(f)
(i)
Calculate the average current in the lightning strike.
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(1)
(ii)
Estimate the energy released during the lightning strike.
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(3)
(Total 18 marks)
4
4.
This question is about the electric potential due to a charged sphere.
(a)
Define electric potential at a point in an electric field.
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(3)
The diagram below shows an isolated, metal sphere in a vacuum that carries a negative electric charge of 9.0 nC.
–
(b)
On the diagram above draw
(i)
arrows to represent the electric field pattern in the region outside the charged sphere.
(3)
(ii)
lines to represent three equipotential surfaces in the region outside the sphere. The potential differences between
the lines are to be equal in value.
(2)
(c)
Explain how the lines representing the equipotential surfaces that you have sketched indicate that the strength of the
electric field is decreasing with distance from the centre of the sphere.
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(2)
5.
This question is about electric fields.
(a)
Define electric field strength.
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(2)
(b)
An isolated metal sphere of radius 50.0 cm has a positive charge. On the diagram below draw lines to represent the
electric field outside the sphere.
50.0 cm
metal sphere
(2)
(Total 4 marks)
5
1.
(a)
(b)
(i)
if independent of charge;
must be gravitational;
(ii)
depends on charge so electric or magnetic;
independent of velocity so electric;
(iii)
(depends on velocity and charge, so) magnetic;
5 max
idea of change in electric potential energy = gain in kinetic energy;
2
qV = ½ mv ;
–19
3
–31 2
14
(1.6 × 10
× 2.1 × 10 ) = (½ × 9.1 × 10
×v ) / v = 7.38 × 10 ;
3
7
–1
Award [0] for v = 2.7 × 10 m s .
2.
(a)
(i)
(ii)
(b)
(i)
lines parallel and normal to plates; (ignore any edge effect)
equally spaced;
direction from (+) to (–);
3
curved path between plates and no curvature outside;
in downward direction;
2
change = qV;
–19
= 1.6 ×10
× 750
–16
= 1.2 × 10
J;
2
Or 750 eV.
(ii)
(c)
(i)
(ii)
3.
(a)
(b)
2
–16
½mv = 1.2 × 10
;
–31
2
–16 2
14
½ × 9.1 × 10
× v = 1.2 ×10
/ v = 2.64 × 10
7
–1
to give v = 1.67 × 10 m s ;
2
inside solenoid, lines parallel to axis;
line spacing about double at ends / lines equally spaced in solenoid;
reasonable shape (symmetry and curving);
correct direction (to left);
4
path with no deviation along axis;
1
there are two types of charge: positive and negative;
if they are moved apart, this is charge separation / OWTTE;
2 max
electric field strength is the force per unit charge;
felt by a positive test charge placed in the field / OWTTE;
2 max
Accept mathematical definitions, but do not award any marks for just copying the formula
from the data booklet. Answers need to define the terms to receive credit.
(c)
straight lines from Earth to negative;
equally spaced;
edge effect shown;
thundercloud
500 m
ground
6
(d)
(e)
(ii)
(e)
correct substitution to calculate σ (= 2.86 × 10
–12
6
–1
E = 20 / (8.85 × 10
× 7 × 10 ) V m ;
5
–1
= 3.2 × 10 V m ;
5
–1
= 3 × 10 V m ;
–6
Cm
–2
);
[1] for each appropriate and sensible assumption eg
edge of cloud parallel to ground;
cloud and ground effectively infinite length;
permittivity of air the same as vacuum;
ground and cloud surface both flat, etc;
5
potential difference = 3.2 × 10 × 500 V;
8
= 1.6 × 10 V;
3 max
2 max
2 max
8
Accept 1.5 × 10 V.
(f)
(i)
(ii)
average current = 20 C / 20 ms
= 1000 A;
average p.d.
energy released
1
8
8
= 1.6 × 10 V / 2 = 0.8 × 10 V;
8
= average p.d × charge = 0.8 × 10 × 20;
9
= 1.6 × 10 J;
3 max
9
[2] if maximum p.d. used to get 3.2 × 10 J.
[18]
4.
(a)
the work done per unit charge;
in bringing a small positive charge;
from infinity to that point;
3
A completely accurate definition is necessary for [3 max].
(b)
(i)
–
(ii)
(c)
sufficient arrows to show decreasing radial field;
direction;
no field in the centre;
3
three concentric circles;
with increasing radii;
2
since field strength is the gradient of potential;
E must be decreasing;
or
some recognition that if the field were constant for example;
the lines would be equally spaced;
OWTTE;
2 max
Allow [1 max] for bald statement “spacing between equipotentials is increasing” /OWTTE.
5.
(a)
(b)
force per unit charge;
exerted on a small positive test charge / small positive charge /
positive point charge;
at least four radial lines evenly spaced around the sphere;
with arrows away from centre;
Award [1 max] if any lines inside sphere.
2
2
[4]
7