Download Q1: Which of the following graphs represents the magnitude

Phys102
Term: 131
Online HW-Ch23-Lec03
Q1:
Which of the following graphs represents the magnitude of the electric field as a
function of the distance from the center of a solid charged conducing sphere of radius
R?
Ans:
E
Q2:
A proton is shot directly toward the center of a large metal plate that has surface
density 2.0 x 10-6 C/m2. If the initial kinetic energy of the proton 1.6 x 10-17 J and if
the proton is to stop just as it reaches the plate, how far from the plate must be
launched? (Give the answer in three significant figures and SI units)
Ans:
We take the initial direction of motion of the proton to be positive. Then, the electric
field is given by E = σ/ε 0 , where σ is the surface charge density on the plate. The
force on the electron is F = –eE = –eσ/ε 0 and the acceleration is:
a=
F
eσ
= −
m
ε 0m
where m is the mass of the proton. The force is constant, so we use constant
acceleration kinematics. If v 0 is the initial velocity of the proton, v is the final velocity,
and x is the distance traveled between the initial and final positions, then
v 2 − v02 =
2ax. Set v = 0 and replace a with –eσ/ε 0 m, then solve for x. We find:
v 2 ε 0 mv02
− 0 =
x=
.
2a
2eσ
Now
1
2
mv02 is the initial kinetic energy K 0 , so
=
x
ε 0 K0
=
eσ
(8.85 ×10 C / N ⋅ m )(1.60 ×10 J )
(1.60 ×10 C )( 2.0 ×10 C/m )
−12
2
−19
−17
2
−6
2
= 4.43 × 10−4 𝑚
KFUPM-Physics Department
1
Phys102
Term: 131
Online HW-Ch23-Lec03
Q3:
A charge is distributed uniformly along a long straight wire. If the electric field 4.0
cm from the wire is 40 N/C, then the electric field 8.0 cm from the wire is (Give the
answer in two significant figures and SI units)
Ans:
E1 =
λ
2π × ε 0 × r1
E2 =
λ
2π × ε 0 × r2
E2 r1 4
= = = 0.5
E1 r2 8
⇒ E2 = 20 N/C
KFUPM-Physics Department
2