Introductory Physics Volume Two

A Hints 183
4.12 Consider the vector nature of the definition of work and the
direction of the velocity relative to the magnetic force.
4.13 Write out the vectors ⃗ L for each line segment and then do the
cross products.
5.1 Try plotting points for various values of t to get a sense of the
function.
5.2 Start with ⃗r(t) = ⃗a + btî + ct 2 ĵ and find the value of the constants
by demanding that the curve goes through the three given points.
5.3 The parameterization is tî
5.4 The parameterization is a cos tî + a sin tĵ.
5.5 Since the current density is not uniform, I in = ∫ JdA.
5.7 Use the result B = µ 0 I/2πr.
5.8 Use the Biot-Savart law.
5.9 Use the method of the previous problem, and also note that the
current can be found from the electron speed and the radius of the
orbit.
5.10 First argue that half of the wire does not produce any field at
the point of interest. Then use the Biot-Savart law on the other half.
5.11 Argue that the radial lines do not contribute. Note that the
field due to the two arcs are in opposite directions to each other.
5.12 First find the field created by wire 1 at the location of wire 2.
Then find the force that this field produces on wire 2.
5.13 Use Ampere’s Law.
5.14 Use Ampere’s Law.
5.15 Since the current density is not uniform, I in = ∫ JdA.
6.1 The induced current is in the same direction as the electric field.
Determine the direction of the induced field in the center of the loop,
from the known electric field direction. Compare the induced field with
the existing field.
6.2 Choose the Amperian loop to be a circle with radius r and going
through the desired field point half way between the plates. Note that
the current density between the plates is zero.
6.3 Use Kirchhoff’s loop rule to write an equation in the current and
the derivative of the current. Try a solution of the form I(t) = a+be −αt .
6.4 The RMS voltage of the source in the a standard outlet is 120
volts.
6.5 Follow the example in the text for an RC circuit.