Question

# 10. A spherical conductor of radius R = 1.5cm carries the charge of 45μ, (a) What...

10. A spherical conductor of radius R = 1.5cm carries the charge of 45μ,
(a) What is the charge density (ρ) of the sphere?
(b) Calculate the electric field at a point r = 0.5cm from the center of the sphere.
(c) What is the electric field on the surface of the sphere?
11. Two capacitors C1 and C2 are in series with a voltage V across the series combination.
Show that the voltages V1 and V2 across C1 and C2, respectively are:
V1 = [C2 /(C1 + C2)]V and V2 =[C1/(C1 + C2)]V
12. The electric field due to an infinite line of charge is perpendicular to the line and has
magnitude
E =λ / (2πℇ₀r)
Consider an imaginary cylinder with radius r = 0.250m and length l = 0.400m that has an
infinite line of positive charge running along its axis. The charge per unit length on the
line is λ = 6.00 μC/m
(i) What is the electric field due to the cylinder due to this infinite line of charge?
(ii) What is the flux through the cylinder if its radius is increased to r = 0.500m?
(iii) What is the flux through the cylinder if its length is increased to l = 0.800m?
13. A point charge q1 = 4.00nC is located on the x-axis at x = 2.00m, and a second charge
q2 = −6.00nC is on the y-axis at y = 1.00m. What is the total electric flux due to these
two point charges through a spherical surface centred at the origin with radius
(a) 0.500m, (b) 1.50m and (c) 2.50m?
14. A hollow, conducting sphere with an outer radius of 0.250 m and an inner radius of
0.200 m has a uniform surface charge density of +6.37−6C/m2. A charge of −0.500 μC is
now introduced in to the cavity inside the sphere.
(a) What is the new charge density on the outside of the sphere?
(b) Calculate the strength of the electric field just outside the sphere.
(c) What is the electric flux through a spherical surface just outside the inner surface of the
sphere?
15. Three point charges, which initially are infinitely far apart, are place at the corners of an
equilateral with sides d. Two of the point charges are identical and have a charge q. If zero
net work is required to place the three charges on the corners of the triangle, what must the
value of the third charge be?
16. A charge is 28.0nC is placed in a uniform electric field that is directed vertically upwards
and has a magnitude of 4.00×104 V/m. What work is done by the electric forces when the
charge moves
(a) 0.450 m to the right, (b) 0.670 m upwards,
(c) 2.60 m at an angle 45o downwards from the horizontal?
17. The potential due to a point charge Q at the origin may be written as
?=?4????=Q4πϵo( x2+?2+?2)^1/2
(a) Calculate Ex, Ey, and Ez using
Ex =∂V/ ∂x, Ey =∂V/ ∂y, Ez =∂V/ ∂z
(b) Show that the results of part (a) agrees with the equation
?=Q4πϵor²
for the electric field of a point charge.
18. Two parallel plate have equal and opposite charge. When the space between the plates is
evacuated, the electric field is E = 3.20×105 V/m. When the space is filled with dielectric,
the electric field is E = 2.50×105 V/m.
(a) what is the charge density on each surface of the dielectric?
(b) What is the dielectric constant?
19. A parallel plate capacitor of separations distance d between the plates has the space
between filled with two slabs of dielectrics, one with constant κ1 and the other with constant
κ2.
(a) Each slab has thickness d/2, show that the capacitance is given by
(b) The thickness of each slab is the same as the plate separation d, and each slab fills half of the volume between the plates. Show that the capacitance is
?=???(?1+?2)2?

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