Electric and Magnetic Fields: Energy, Momentum and Angular Momentum

Electric and magnetic fields are said to carry energy, momentum and angular momentum. Under what conditions is this true? What is the total angular momentum in this system of two charged canisters of radii a and b and a long solenoid carrying current I with n turns per unit length and a radius R. Figure 1



QUESTIONS

(Score is number right minus number wrong.)

The Poynting vector is non-zero only when electric and magnetic fields are exactly perpendicular to one another.
True
False
The only momentum in this system is the momentum of the moving electrons of the current I in the windings of the solenoid.
True
False
The Poynting vector represents an average flow of electromagnetic energy for time varying fields only.
True
False
There cannot be an energy current and momentum density given by the Poynting vector in this system unless the electric and magnetic fields change with time.
True
False
The energy current and momentum density given by the Poynting vector in this system would reverse direction if the actual charge carriers were positive instead of the negative electrons (with the current remaining in the same direction as shown).
True
False
The Poynting vector gives a correct magnitude of energy flow, but does not necessarily give the correct direction unless the energy is carried by electromagnetic waves where electric and magnetic fields are perpendicular to one another. For this reason, the Poynting vector for the energy moving along a straight current carrying wire from a battery to a load resistor has the right magnitude but the direction is incorrectly given by the Poynting vector as coming in from infinity perpendicular to the wire.
True
False
The Poynting vector vanishes everywhere in this system except where,
Equation (4a).
Equation (4b).
Equation (4c).
Equation (4d).
The direction of the electromagnetic momentum density in this system is in the direction of
Equation (5a).
Equation (5b).
Equation (5c).
Equation (5d).
Equation (5e).
Equation (5f).
The direction of the electromagnetic momentum density in this system is in the opposite direction to the motion of the electrons creating the current I. Thus, the net momentum in this system vanishes.
True
False
The direction of the electromagnetic angular momentum density in this system (relative to the symmetry axis) is in the direction of
Equation (5a).
Equation (5b).
Equation (5c).
Equation (5d).
Equation (5e).
Equation (5f).
The magnitude of the total electromagnetic angular momentum in this system is
Equation (6a)
Equation (6b)
Equation (6c)
Equation (6d)

Imagine that the charged cylinders are free to rotate about the symmetry axis on frictionless bearings. If we now turn off the current, note that dI/dt is instrinsically negative.


If the current in the solenoid is reduced to zero, an electric field will be induced in the direction indicated by
Equation (5a).
Equation (5b).
Equation (5c).
Equation (5d).
Equation (5e).
Equation (5f).
If the current in the solenoid is reduced to zero, the induced electric field at the surface of the cylinder at radius b (=s) will be
Equation (7a).
Equation (7b).
Equation (7c).
Equation (7d).
If the current in the solenoid is reduced to zero, the induced electric field at the surface of the cylinder at radius a (=s) will be
Equation (7a).
Equation (7b).
Equation (7c).
Equation (7d).
If the current in the solenoid is reduced to zero, the torque from the induced electric field at the surface of the cylinder at radius b will be
Equation (8a).
Equation (8b).
Equation (8c).
Equation (8d).
Equation (8e).
Equation (8f).
If the current in the solenoid is reduced to zero, the torque from the induced electric field at the surface of the cylinder at radius a will be
Equation (8a).
Equation (8b).
Equation (8c).
Equation (8d).
Equation (8e).
Equation (8f).
If the current I in the solenoid is discontinued, the charged cylinders will (if they are constrained to rotate together in the direction determined by the net torque)
remain stationary.
rotate in the direction of Equation (5b).
rotate in the direction of Equation (5e).
If the current I in the solenoid is discontinued, the total mechanical angular moment of the rotating charged cylinders should satisfy
Equation (9a).
Equation (9b).
Equation (9c).
The momentum of the electrons creating the current I appears to be inconsequential in this system.
True
False
EQUATIONS

Equations


Equations









Username



Register BEFORE taking the first Quiz!
(Click here to return to the Table of Contents)