Capacitors and Dielectrics
Challenge Problems
Problem 1:
A parallel plate capacitor has capacitance C. It is connected to a battery of EMF until
fully charged, and then disconnected. The plates are th
Maxwells Equations and Electromagnetic Waves
Challenge Problem Solutions
Problem 1:
The magnetic field of a plane electromagnetic wave is described as follows:
B = B0 sin( kx t )
j
a) What is the wav
Capacitors and Dielectrics
Challenge Problem Solutions
Problem 1:
A parallel plate capacitor has capacitance C. It is connected to a battery of EMF until
fully charged, and then disconnected. The plat
Angular Momentum Problems
Challenge Problems
Problem 1: A spaceship is sent to investigate a planet of mass mp and radius rp . While
hanging motionless in space at a distance 5rp from the center of th
Experiment VS Vibrating Systems
Introduction
Many vibrating or oscillating systems around us are visible or audible, but most are hidden. The
motion of a clock pendulum, or of a child on a swing, can
Current, Current Density, Resistance and Ohms Law
Challenge Problems
Problem 1:
A straight cylindrical wire lying along the x-axis has a length L and a diameter d. It is
made of a material described b
DC Circuits with Capacitors
Challenge Problems
Problem 1:
In the circuit shown, the switch S has been closed for a long time. At time t=0 the switch
is opened. It remains open for a long time T, at wh
DC Circuits
Challenge Problems
Problem 1:
A battery of emf has internal resistance Ri , and let us suppose that it can provide the
emf to a total charge Q before it expires. Suppose that it is connect
Magnetic Forces
Challenge Problems
Problem 1:
A particle with charge q and velocity v enters through the hole in screen 1 and passes
through a region with non-zero electric and magnetic fields (see sk
Magnetic Dipoles
Challenge Problems
Problem 1:
Circle the correct answer.
Consider a triangular loop of wire with sides a and b . The loop carries a current I in the
direction shown, and is placed in
Undriven RLC Circuits
Challenge Problems
Problem 1:
Show that
where
A cos t + B sin t = Qm cos (t + ) ,
(
)
Qm = ( A2 + B 2 ) , and = tan 1 B A .
12
Problem 2:
At the moment depicted in the LC circuit
Faradays Law
Challenge Problems
Problem 1:
A coil of wire is above a magnet whose north pole is pointing up. For current, counterclockwise when viewed from above is positive. For flux, upwards is posi
Diffraction
Challenge Problems
Problem 1:
Measuring the Wavelength of Laser Light
Suppose you shine a red laser through a pair of narrow slits (a = 40 m) separated by a
known distance and allow the re
Introduction to Electric Fields
Challenge Problem Solutions
Problem 1:
We have defined a vector field as a family of vectors, with a vector at every point in
space. A scalar field can be likewise defi
Magnetic Field
Challenge Problems
Problem 1:
Consider two bar magnets placed at right
angles to each other, as pictured at left.
(a) If a small compass is placed at point P,
what direction does the pa
Gauss Law
Challenge Problems
Problem 1:
The grass seeds figure below shows the electric field of three charges with charges +1,
+1, and -1, The Gaussian surface in the figure is a sphere containing tw
Experiment FL Flow
Introduction
Steady flows are driven by forces that are balanced by resisting forces. For instance, the amount
of water coming out of a shower depends on the water pressure as provi
Mechanics
Experiments from Kits
Peter Dourmashkin
John G. King
Mechanics Experiments from Kits
Peter Dourmashkin
Senior Lecturer in Physics
Massachusetts Institute of Technology
John King
Francis Frei
Introduction to Electric Fields
Challenge Problems
Problem 1:
We have defined a vector field as a family of vectors, with a vector at every point in
space. A scalar field can be likewise defined as a
Math Review
Challenge Problems
Problem 1:
Triangle Identity
Two sides of the triangle in Figure 1 form an angle . The sides have lengths a and b .
Figure 1: Law of cosines
The length of the opposite s
Electric Fields, Dipoles and Torque
Challenge Problems
Problem 1:
Three charges equal to Q, +Q and +Q are
located a distance a apart along the x axis (see
sketch). The point P is located on the positi
Electric Potential, Discrete and Continuous Distributions of Charge
Challenge Problems
Problem 1:
Two point-like charged objects with charges +Q and Q are placed on the bottom
corners of a square of s
Electric Potential, Equipotential Lines and Electric Fields
Challenge Problems
Problem 1:
A graph of the electric potential V ( z ) vs. z is shown in the figure below.
Which of the following statement
Capacitance & Capacitors, Energy Stored in Capacitors
Challenge Problems
Problem 1:
A parallel-plate capacitor is charged to a potential V0, charge Q0 and then disconnected
from the battery. The separ
Conductors and Insulators, Conductors as Shields
Challenge Problems
Problem 1:
Part of the lab this week involves shielding. We have a visualization to help you better
understand this. Open it up:
htt
Maxwells Equations and Electromagnetic Waves
Challenge Problems
Problem 1:
The magnetic field of a plane electromagnetic wave is described as follows:
B = B0 sin( kx t )
j
a) What is the wavelength o
Electric Fields and Continuous Charge Distributions
Challenge Problem Solutions
Problem 1:
Two thin, semi-infinite rods lie in the same plane. They make an angle of 45 with each
other and they are joi
Creating Fields: Biot-Savart Law
Challenge Problem Solutions
Problem 1:
Find the magnetic field at point P due to the following current distributions:
(b)
(a)
Problem 1 Solution:
G
(a) The fields due
Introduction to Electric Fields
Challenge Problem Solutions
Problem 1:
Vector fields
Make a plot of the following vector fields:
(a) v = 3 5
ij
(b) v = r
(c) v =
r
r2
3x y 2 y 2 x 2
(d) v = 5 i +
j
r
RL Circuits
Challenge Problem Solutions
Problem 1:
RL Circuits
Consider the circuit at left, consisting of a battery (emf
), an inductor L, resistor R and switch S.
For times t<0 the switch is open an