Electric Fields and ForceAssess. Statements 6.2.1-6.2.8 due Monday, 10/20/14

Electric Fields Like the gravitational field around masses, an

electric field occupies the space surrounding charged objects.

To test for the presence of an electric field:o Bring a small positive charge (q) into the spaceo Release the small positive charge

• If the charge experiences a force, then we know there is an electric field present

• No force, no electrical field

Known as a Test Charge

What happens when a test charge is brought near a

negatively charged object? Attractive forces The test charge will accelerate towards the

negatively charged object

The test charge will follow the path of the electric field of the negative object:

Electric Force--quantified

Electric charges exert forces on other electric charges through the electric fields

Quantified through Coulomb’s Law:o The electric force between two point charges,

Q1 and Q2, is inversely proportional to the square of their separation distance and directly proportional to the product of the two charges:

e0electric permittivity of a vacuum o (= 8.85 x 10-12 C2·N-1·m-2)

𝐹=𝑘𝑄1𝑄2

𝑟 2

N·m2·C-2

Sample Problem: Two charges, 4.00 mC and 6.00 mC, are placed

along a straight line separated by a distance of 2.00 cm. Find the force exerted on each charge.

𝑞1=4.00×10− 6𝐶

𝐹=(8.99×10− 9)(4.00×10−6)(6.00×10− 6)

0.02002

𝐹=𝑘𝑄1𝑄2

𝑟 2

Sample Problem #2 Two equally charged lightweight balls, q, are

suspended from strings that are each 10.0 cm long. They repel each other and have a separation distance between the charged particles is 14.00 cm. Assume the mass of each of the lightweight balls is 0.575 g. What is the charge on each of the balls?

Electric Fields Electric field lines are drawn in the same direction as

the force the small postive test charge would experience at that point.

The electric field strength is defined as the force per unit charge experienced by a small positive test charge, q.

The electric field strength is FELT by the charge in the field itself.

The electric field strength is CAUSED by the charge creating the field

𝐸=𝐹𝑞

Other ways to look at electric field:

Electric field strength depends on the charge that is creating the field, and it depends on how far away from the charge the field is being measured:

𝐹=𝑘𝑄1𝑄2

𝑟 2

𝐸=𝐹𝑞

𝐴𝑠𝑠𝑢𝑚𝑒𝑄2 𝑖𝑠 h𝑡 𝑒𝑠𝑎𝑚𝑒𝑎𝑠𝑞

Sample Problem—electric fields

What is the electric field strength 7.50 cm from a particle with a charge of 5.00 mC?

What force would a charge of +1.00 nC experience at that point?

Sample problem #4 The electric field between two parallel plates is

100.0 N·C-1. What acceleration would a charge of 2.00 mC and mass 1.00 x 10-3 kg experience if placed in this field? (ignore the weight of the charged mass)

Electric Potential Imagine an electric field generated by a charge

Q, and consider a positive test charge, q, in that field.

What must be done to move q closer to Q?

Electric Potential is the work done per unit charge to bring a positive test charge from far away to the some point P in an electric field created by Q

The work done in moving the charge to point P from infinity increases the electrical potential energy of the test charge.

𝑉=𝑊𝑞

Sample Problem #5 The work done in moving a test charge of 2.0 mC

from very far away to a point P is 1.50 x 10-8 J. What is the electric potential at point P?

Sample Problem #6 The potential at a point P is 12.0 V and a charge

of 3.00 C is placed there. What is the electric potential energy of the charge?

What is the electric potential energy if the charge placed at P is – 2.00 C?

Potential Difference Electric potential difference: the work done to

move a charge from point A in an electric field to point B in an electric field (neither is very far away from the source of the field).

Mathematically, it’s the difference of potential energy for the charge at each of the positions (W = DU)

Potential difference is the total work done to move the charge (change in energy)

Potential is the work per unit charge.

Sample Problem #7 What work must be performed in order to move a

charge of 5.00 mC from the negative plate to the positive plate if a potential difference of 250. V is established between the plates?

Sample problem #8: conservation of energy

A charge of 5.00 mC and mass 2.00 x 10-8 kg is shot with an initial velocity of 3.00 x 102 m·s-1 between two parallel plates kept at a potential of 200.0 V and 300.0 V, respectively. (the charge starts at the low potential end)

o What will the speed of the charged mass be when it gets to the other (higher potential) plate?

Electronvolt The amount of work needed to move a charge

equal to one electron’s charge through a potential difference of exactly 1 volt.

What is the work needed to move a charge of +2e across a potential difference of 2.0 V?

What is the work needed to move a charge of +3e across a potential difference of 5.0 V?

Electronvolts and Joules

What is the equivalent of 1 eV, measured in Joules?

1 eV = work to move 1e through 1V What’s the charge of 1e?

W = qV=(1.61x10-19 C)·(1 V) = 1.61 x 10-19 J