Question

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

?=2ϵoAd( k1k2K1+k2)

(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?

Answer #1

A
solid spherical charge insulator of radius R carries a uniform
charge density of p.
A) Derive an equation for the electric field as a function of
the radical position inside the sphere using electric flux
and a Gaussian surface of variable radius.
B) Derive an equation for the electric field as a function of
the radial position outside the sphere.
C) Multiply your results from parts A and B with some test
charge, are these results consistent with
coulombs...

A) A 1 nano Coulomb spherical charge has a radius of 10
centimeters. The charge is uniformly distributed throughout the
volume of the sphere.
Find the electric flux through a spherical gaussian surface
centered on the charge with a radius of 1 meter. Answer in units of
(N*m^2)/C.
B) Same as part A, but let the Gaussian surface be a 1 meter
cube centered on the charge.
C) What is the strength of the E field on the surface of...

1. A spherical balloon is inflated to a radius of R. It is given
a charge of Q so that it has a uniform surface charge density of σ.
At some point, P, fairly far from the balloon the electric field
strength due to the balloon is measured to be E.
(a) The balloon is electrically isolated so that no charge can
flow onto or off of it. While it is isolated it is inflated to a
radius of 2R....

A hollow, spherical, ideal insulator (R=0.075m) has a net charge
of +3.75μC, with the charge is distributed uniformly throughout its
volume
A- Calculate the total electric flux though a “Gaussian” sphere
(with radius r=0.065m) centered on the center of the charged
sphere.
B- Find the magnitude and direction of the electric field at a
point, r=0.115m, directly below the center of the sphere.

A point charge q = +3 µC is at the center of a sphere
of radius 0.9 m.
(a) Find the surface area of the sphere.
___m2
(b) Find the magnitude of the electric field at points on the
surface of the sphere.
___N/C
(c) What is the flux of the electric field due to the point charge
through the surface of the sphere?
___ N · m2/C
(e) What is the net flux through a cube of side 2...

A point charge q1 = 4.05 nC is located on the x-axis at
x = 2.30 m, and a second point charge q2 = -6.80 nC is on the
y-axis at y = 1.00 m.
A) What is the total electric flux due to these two point
charges through a spherical surface centered at the origin and with
radius r1= 0.800 m?
B) What is the total electric flux due to these
two point charges through a spherical surface centered...

A point charge q1 = 3.65 nC is located on the
x-axis at x = 2.30 m , and a second point charge
q2= -6.10 nC is on the y-axis at y =
1.30 m.
(a) What is the total electric flux due to these two point
charges through a spherical surface centered at the origin and with
radius r1 = 0.435 m ?
(b) What is the total electric flux due to these two point
charges through a spherical...

A point charge q1 = 3.50 nC is located on the x-axis at
x = 1.90 m, and a second point charge q2 = -5.60 nC is on the
y-axis at.y = 1.10 m.
What is the total electric flux due to these two point charges
through a spherical surface centered at the origin and with radius
r1 = 0.635 m?
What is the total electric flux due to these two point charges
through a spherical surface centered at the...

A hollow, conducting sphere with an outer radius of 0.260 m and
an inner radius of 0.200 m has a uniform surface charge density of
+6.47 × 10−6 C/m2. A charge of -0.400 μC is now introduced into 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
inside the inner surface...

A hollow, conducting sphere with an outer radius of 0.260 m and
an inner radius of 0.200 m has a uniform surface charge density of
+6.37 × 10−6 C/m2. A charge of -0.700 μC is now introduced into 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 inside...

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