Download exercises.electrostatics.2

APHY112
Exercises
Coulomb’s Law, Electric Field, charge motion, general problems
Useful info:
1
4o
 9  10 9
Nm 2
C2
1. Charged spheres moved. Two charged spheres are 15.59 cm apart. When they are
moved, the force on each of them is found to have been tripled. How far apart are they
now?
2. Electrons in water. What is the total charge of all the electrons in 1 kg of water?
3. Charges in a triangle. Three charged particles are placed at the corners of an
equilateral triangle of side 120 m (see Fig.1). Calculate the magnitude and direction of
the net force on each charge due to the two.
Fig. 1
Fig. 2
Q1 = +4 μC
L
L
θ
θ
r = 120 cm
Q2 = -8 μC
Q2 = -6 μC
m, q
m, q
4. Charged spheres hung. Two identical spheres of mass m are hung from silk threads
of length L, as shown in Fig. 2. Each sphere has the same charge q. The radius of each
sphere is very small compared to the distance between the spheres, so they may be treated
as point charges. Show that if the angle θ is small, the equilibrium separation d between
the spheres is d  (q 2 L / 2o mg )1 / 3 . (Hint: if θ is small, then tan   sin  )
5. Zero electric field. Two unknown point charges are separated by distance L. At a
point on the line joining them, with distance L/3 from Q1 to Q2, the electric field is zero.
What is the ratio Q1/Q2?
6. Proton in electric field. A uniform electric field exists in the region between two
oppositely charged parallel plates. A proton is released from rest at the surface of the
positively charged plate and strikes the surface of the opposite plate, 1.6 cm distant from
the first, in a time interval of 1.5  10 6 s . Find i) the magnitude of the electric field and ii)
the speed of the proton when it strikes the negatively charged plate.
7. Charged sphere in equilibrium. A small, 2 g plastic sphere is suspended by a L=20
cm long string in a uniform electric field E = 1000 N/C as shown in Fig. 3. If the sphere
is in equilibrium when the string makes a θ =15.° angle with the vertical, what is the net
charge on the sphere?
Fig. 3
Fig. 4
L=20cm
θ
m=2g
q=?
L
L
θ
E
q1 = -50 nC
θ
E=?
q2 = +50 nC
8. Spheres in electric field. Two small spheres, each of mass 2 g, are suspended by
light strings L=10 cm in length (Fig. 4). A uniform electric field is applied in the x
direction. The spheres have charges equal to -50 nC and +50 nC. Determine the electric
field that enables the spheres to be in equilibrium at an angle of θ = 10°.
9. Proton in electric field. A proton accelerates from rest in a uniform electric field
of 640 N/C. At some later time, its speed is 1.2  10 6 s (i) Find the acceleration of the
proton. (ii) How long does it take the proton to reach this speed? (iii) How far has it
moved in this time? (iv) What is its kinetic energy at this time?