Name:_______________________ ___
H-ITT or pseudonym: ______________
PHY2061
9-23-04
Exam 1
Closed book exam. A calculator is allowed.
Exam is worth 100 points, 25% of your total grade.
UF Honor Code: “On my honor, I have neither given nor received unauthorized aid in doing
this exam.”
K=
1
= 9 ×109 N m 2 / C 2
ε 0 = 8.8542 × 10−12 C2 / N m 2
4πε 0
q
qq
ρ
Φ = v∫ Ε ⋅ dΑ = enc ∇ ⋅ E =
F = K 1 2 2 rˆ12
S
ε0
ε0
r
F
U
E=
V=
W = −∆U = ∫ F ⋅ ds
C
q0
q0
∂
∂
∂
∇ = xˆ + yˆ + zˆ
∂x
∂y
∂z
Q = C ∆V
F = grad ( f ) = ∇f
∇ ⋅ F = div ( F ) =
∂Fx ∂Fy ∂Fz
+
+
∂x
∂y
∂z
∫
V
∇ ⋅ F dV = v∫ F ⋅ dΑ
Page 1 of 11
S
e = 16022
.
× 10−19 C
E = −∇V
∆V = − ∫ E ⋅ ds
C
1
Q2
2
U = C ( ∆V ) =
2
2C
Name:_______________________ ___
H-ITT or pseudonym: ______________
PHY2061
9-23-04
y
q1
a
a
q2
q3
x
1. Consider 3 point particles with electrical charge arranged in the form of an equilateral
triangle as shown. The side length is a = 5 cm, and the top particle has charge
q1 = +2µC while the bottom two particles have charge q2 = q3 = +1 µC
( 1µ C = 10-6 C ).
(a) [4 points] What is the direction of the force acting on particle 1
(the one at x = 0 and y > 0)?
(b) [8 points] Calculate the magnitude of the force acting on particle 1.
Page 2 of 11
PHY2061
9-23-04
Name:_______________________ ___
H-ITT or pseudonym: ______________
1. Continued:
(c) [6 points] Calculate the electric field at the location of particle 1 arising from
particles 2 and 3 ?
(d) [6 points] Does a position exist where a fourth charge can be added to put the
triangle in electrostatic equilibrium? If so, sketch where it would lie
approximately, and write down an equation for its charge in terms of:
the distance d from particle 1, the side length a, and the magnitude of the
other charges (in other words, you don’t have to solve for d).
Page 3 of 11
Name:_______________________ ___
H-ITT or pseudonym: ______________
PHY2061
9-23-04
y
R
x
2. Consider electric charge distributed along a one-dimensional path in the form of a
semi-circle with radius R = 5 m in the upper two quadrants of the x-y plane as shown.
The semicircle has a center at (x, y) = (0,0) and has a linear charge density of λ =
+2µC/m.
(a) [6 points] Find component of the electric field along the x-axis (Ex) at the
origin (0,0).
(b) [6 points] Find component of the electric field along the y-axis (Ey) at the
origin (0,0).
Page 4 of 11
PHY2061
9-23-04
Name:_______________________ ___
H-ITT or pseudonym: ______________
2. Continued:
(c) [6 points] If a semi-circle is added to the lower two quadrants (y < 0, with the
center at the origin again) with a linear charge density of equal magnitude but
opposite sign to the upper semicircle (i.e. −2µC/m), calculate the total Ex and
Ey at the origin again arising from both semicircles.
Page 5 of 11
Name:_______________________ ___
H-ITT or pseudonym: ______________
PHY2061
9-23-04
y
x
z
3. Consider a cube with side length s = 3.0 m and one corner at the origin (0,0,0) as
shown.
(a) [6 points] What is the total electric flux emanating out through the surface of
the cube if the electric field is E = 15 zˆ N/C ? ( ẑ is a unit vector pointing in
the z-direction.)
(b) [6 points] What is the total electric flux emanating out through the surface of
the cube if the electric field is E = ( 5 x 2 xˆ + 15 z zˆ ) N/C-m ?
Page 6 of 11
PHY2061
9-23-04
Name:_______________________ ___
H-ITT or pseudonym: ______________
3. Continued:
(c) [6 points] What is the total charge enclosed by the cube if the electric field is
the same as in part (b)?
(d) [6 points] What is the electric charge density at the center of the right face at x
= 3.0 m if the electric field is the same as in part (b)?
Page 7 of 11
Name:_______________________ ___
H-ITT or pseudonym: ______________
PHY2061
9-23-04
y
b
a
x
4. A very long cylinder (length L = 5 m) carrying a total electric charge of +5µC
distributed uniformly along its length is surrounded by a concentric cylindrical shell
with a total charge of −2.5µC distributed uniformly along its length as shown. The
radius of the inner cylinder is a = 0.005 m and the radius of the outer cylinder is b =
0.01 m.
(a) [6 points] What is the electric field strength and direction between the two
cylinders (a<r<b) ?
(b) [6 points] What is the electric field strength and direction outside the outer
cylinder (r>b) ?
Page 8 of 11
PHY2061
9-23-04
Name:_______________________ ___
H-ITT or pseudonym: ______________
5. [4 points] The figure below shows an object made of an electrically conductive
material with a total electrical charge +Q deposited on it. Sketch the electric field
lines and equipotential lines near the surface of the object.
Page 9 of 11
PHY2061
9-23-04
Name:_______________________ ___
H-ITT or pseudonym: ______________
6. The surface of a conducting sphere of radius 5 cm is at a potential of 450 V with
respect to the potential at infinity.
(a) [6 points] What is the electric charge density on the surface of the sphere?
(b) [6 points] What is the strength of the electric field at a distance of 10 cm
above the surface of the sphere?
Page 10 of 11
PHY2061
9-23-04
Name:_______________________ ___
H-ITT or pseudonym: ______________
(c) [6 points] If another sphere is brought in with a potential of −450 V at its
surface with respect to infinity, what is the capacitance of the two-sphere
system?
Page 11 of 11