Ch. 21 Electric Forces & Fields

AP Physics C

1. Pith Ball Lab Sample Problem

Problem 2:

• An electrically neutral penny, of mass 3.11 g, contains equal amounts of positive and negative charge. Assuming the penny is made entirely of copper, what is the magnitude q of the total positive (or negative charge) charge in the penny?

• http://www.webelements.com/

Problem 3:

• The average distance between the electron and the central proton in the hydrogen atom is 5.3 x 10-11 m.• What is the magnitude of the

average electrostatic force that acts between these two particles?

• What is the magnitude of the average gravitational force that acts between these particles?

Charges & Fields:

• http://phet.colorado.edu/simulations/sims.php?sim=Charges_and_Fields

• Electric field: Oppositedly charged parallel plates

Problem 6:

• The diagram below shows a charge +8q at the origin of an x-axis and a charge of -2q at x = L. At which points is the net electric field due to these two charges zero? 

Problem 7:

• The nucleus of a uranium atom has a radius R of 6.8 fm. Assuming that the positive charge of the nucleus is distributed uniformly, determine the electric field at a point on the surface of the nucleus due to that charge. (Note: 1 fm = 1 x 10-15 m; The atomic mass unit for uranium is 92.)

Continuous distribution of charge:

• Electric Field due to a continuous distribution of charge:• Charge per unit length:

• Charge per unit surface:

• Charge per unit volume:

dq

ds

dq

dA

dq

dV

A ring of uniform positive charge

• http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/electrostatics/09-RingIntegration/RingIntegrationFullScreen.htm

• Through the use of integration, determine the total electric field at a point that is x from the center of a continuous ring of positive charge, Q, that has a radius of R.

Problem 10:

• A plastic rod having a uniformly distributed charge of –Q. The rod has been bent in a 120o circular arc of radius r. The coordinate axes are placed such that the axis of symmetry of the rod lies along the x-axis and the origin is at the center of curvature of the rod. In terms of Q and r, what is the electric field due to the rod at the origin of the axes?

Problem 11:

• In the Millikan’s oil-drop apparatus, a drop of radius 2.76 μm has an excess charge of three electrons. What are the magnitude and direction of the electric field that is required to balance the drop so it remains stationary in the apparatus? The density of the oil is 920 kg/m3.

Problem 12:

• Determine the path that the proton will follow.

• If the proton is entering the electric field of 10 N/C at the positive plate, how far does it move vertically if the plates are 10 cm long?

Applications of uniform electric fields:

Ink-Jet Printer Cathode-Ray Tube

13. Electric dipole in a uniform E-Field

• What is the net force acting on the dipole?

• What is the net torque about the center of the rod?

13. Electric dipole in a uniform E-Field

• The dipole moment, p, is define to be:• p = qd, where d =

L.• Its direction is

from the net negative charge towards the net positive charge.

13. Potential energy of an electric dipole

• The potential energy of an electric dipole is associated with the orientation of the electric dipole in an electric field.

13. Potential energy of an electric dipole

• The dipole is at its lowest potential energy when it is in its equilibrium orientation, which is when its moment p is parallel with the E-field and the torque is zero.

• This position is called stable equilibrium.

13. Potential energy of an electric dipole

• Its greatest potential energy is when p is perpendicular to the E-field and the torque has a maximum value.

• This is referred to as an unstable equilibrium position.

13. Work done by the external field on the dipole

• Potential is defined as:

2

1

2

1

2 1

sin

[ cos ( cos )]

U W d

U W pE d

U pE

cosU pE p E

Problem 14:

• A neutral water molecule in its vapor state has an electric dipole moment of 6.2 x 10-30 C-m.• How far apart are the molecule’s centers of

positive and negative charge?• If the molecule is placed in an electric field of

1.5 x 104 N/C, what maximum torque can the field exert on it?

• How much work must an external agent do to turn this molecule end for end in this field, starting from its fully aligned position, for which θ = 0?