Download Midterm I - Practice Problems 1 Forces in Helium Atoms 2

Physics 2220 (Spring 2011)
Midterm I - Practice Problems
Mike McLaughlin
Quick Note: At the time of publication of this document, I have not yet seen the
Midterm Exam. The practice problems in this document are what I would consider useful
problems for you to study in preparation for the exam. Your studying approach should not
be limited to working through this set of problems, nor should you interpret these problems
as an official study guide for your exam.
1
Forces in Helium Atoms
An electron (charge of - e) circulates around a helium nucleus (charge of + 2e) in a helium
atom. Which particle (electron of nucleus) exerts the larger force on the other?
2
Electrostatic Forces
If the electrostatic force between two particles has a magnitude of 5.70 N, and the charges
on these particles are 26µC and -47µC, how far apart are the particles? If these particles
live on the x-axis, in what direction does the net electric field field point at a point centered
between the two particles?
3
Zero Acceleration
Two charges, q1 and q2 , are placed on the x-axis at x = −a and x = +a respectively.
A charge Q is now placed at the location x = + a2 . If you want this charge Q to remain
stationary (zero acceleration), what must be the relationship between q1 and q2 ?
4
Two Tiny Balls
Two small conducting balls of equal mass and charge (m and q) hang from the same point
using nonconducting threads of length L. The threads each make an angle θ as measured
from the vertical. Show that the separation, x, between the two balls is given by:
x=
q2 L
2π0 mg
13
(1)
Since the separation is expected to be small then θ will be small. When θ is small, tan θ
can be approximated with sin θ.
5
A Penny Saved...
How many electrons would you have to remove from a penny to give it a net charge of
+1.0 × 10−7 C. To what fraction of a penny’s total number electrons does this correspond?
6
Point Charge - Electric Field
What is the value of charge on a point particle if the electric field at a distance of 50 cm
is determined to be 2.0 N
C?
7
Rhythm of My Heart
A nonconducting rode of length L has a charge of −q spread out uniformly on its length.
Consider the rod to live on the x-axis and determine the electric field due to this rod at a
point P on the x-axis a distance a from the end of the rod. What happens if the point P
is very far away from the rod? Does your math agree?
8
Particle Acceleration
What is the acceleration of an electron in a uniform electric field with magnitude 1.4×106 N
C?
1
How long would take this electron starting at rest to attain a speed equal to 10
that of the
speed of light?
9
Not Your Grandmother’s Pendulum
A uniform electric field is setup using two charged horizontal parallel plates. An insulated
thread is used to hang a small insulating sphere of mass m and charge q from the top
plate. The thread has a length of L. What is the period of the pendulum if the top plate
is negatively charged and bottom plate is positively charged? How does the period change
if you reverse the charges on the plates?
10
I Thought I Was Done With Projectile Motion
Imagine the same plates as in Problem 9. Now, the plates have a length of L, the top
plate is negative, the bottom is positive, and an electric field is established with magnitude
2 × 103 N
C . The separation between the plates is d = 2.00cm. An electron is shot from the
◦
left edge of the lower plate with an initial velocity of 6.00 × 106 m
s at an angle of 45 . Will
the electron strike one of the plates? If so, which plate will it strike and what will be its
x-coordinate upon impact?
11
Too Close for Comfort
If you get very close to the surface of any conductor (regardless of shape), what is the value
of the electric field and in what direction does it point?
12
Rubber
A spherical rubber balloon with a charge of Q uniformly distributed on its surface exists
in your universe. As the balloon is inflated, how does the electric field change inside of the
balloon, outside of the balloon, and at the surface of the balloon.
13
What the Flux?
A point charge, +q, is distance d2 above the center of a square of side d. The square is flat
on the table. What is the magnitude of the electric flux through the square?
14
Irregular
An irregularly shaped conductor has an irregularly shaped cavity inside. A charge q is
placed on the conductor, but there is no charge inside the cavity. Show that there is no
charge on the cavity wall.
15
Coaxial
Two concentric cylindrical shells with radius r = a and r = b have uniform charge densities
(λ) that are equal and opposite spread out along their lengths. Consider a < b and the
interior cylinder to have a negative overall charge. Determine the electric field in three
regions: r < a, a < r < b, and r > b.
16
Spherical Madness
This is a great problem for you to do. A solid sphere of radius a and charge +q uniformly
distributed throughout its volume is concentric with a spherical shell of inner radius b and
outer radius c. This shell has a net charge of −q. Find expressions for the electric field:
(1) inside the sphere where r < a, (2) between the sphere and the shell where a < r < b,
(3) inside the shell where b < r < c, and (4) outside the shell where r > c. Furthermore,
determine the charges on the inside and outside surfaces of the spherical shell.
17
Such Great Potential
The electric field inside a nonconducting sphere of radius R, with charge spread out uniformly throughout its volume, is radially directed and has a magnitude of:
E(r) =
qr
4π0 R3
(2)
Here, q is the charge (positive or negative) in the sphere and r is the distance from the
sphere’s center. Taking V = 0 at the center of the sphere, find the potential V (r) inside
the sphere. What is the difference in electric potential between a point on the surface and
the sphere’s center? If q is positive, which of those two points is at a higher potential?
18
Maggie May
A nonconducting rod of length L and uniform charge density of λ lives in your universe.
Find the electric potential for a point P located a distance d away from midpoint of the
rod.