Electric Fields

What is an Electric Field? An electric field is a region of space surrounding a charged object. A stationary object experiences an electric force in this region because of its charge. It extends outward through space. Every charge is surrounded by both a gravitational and electric field.

Describing an Electric Field Electric fields have magnitude and direction. Electric fields are vector quantities. The magnitude of the field is determined by the strength of the force that is acting on a charge. E = F/q Force is measured in Newtons (N) and charge is measured in Coulombs (C). Electric field strengths are measured in N/C

Sample Problem An electric field is measured using a positive test charge of 5.0 x C. This test charge experiences a force of 2.0 x N on it. What is the magnitude of the electric field at the location of the test charge? E = F/q E = 2.0 x N/5.0 x C E = 40. N/C

Describing an Electric Field What two variables contribute to the strength of an electric field? fields/charges-and-fields_en.html fields/charges-and-fields_en.html Field strength increases as distance decreases and as the magnitude of the charge increases. E = Kq/d 2 (q is the charge producing the field and d is the distance from the charge)

Sample problem What is the magnitude of the electric field strength at a position that is 1.2 m from a point charge of 4.2 x C? E = (9.0x10 9 )(4.2x10 -6 ) (1.2) 2 E = N/C

Picturing an Electric Field The direction of the electric field is identified as the direction the force would exert on a small POSITIVE test charge. Vector diagrams are used to represent electric fields. Not possible to show every vector so field lines, or lines of force, are used to represent electric fields. Field lines point away from positive charges and toward negative charges. and-fields_en.html and-fields_en.html Lines drawn far apart represent weak fields. Lines drawn close together represent strong fields.

Electric Fields and Conductors An electric field is equal to zero inside a conductor. Excess charge resides on the surface. The electric field is perpendicular to the surface. If irregularly shaped, charge accumulates where the surface is smallest-for example at sharp points.

Point to Ponder Is there a limit to how strong an electric field could be? Yes there is a limit. The production of a field depends on a collection of charges. After reaching a certain density, these charges would begin to repel each other. Examples of electric field strength- -field in a fluorescent tube- 10 N/C -field produced by a lightning bolt-10,000 N/C -field produced by an electron in a hydrogen atom- 51, 000 N/C

Energy and Electric Potential When charges move because of a force, work is done. If work is done on a charge, potential energy is gained. (For example; separating two unlike charges, or moving two like charges together). If the work is done by the charge, potential energy is lost. (For example; separating two like charges, or moving two unlike charges together).

Electric Potential Difference Electric potential difference (∆V) is defined as the work done in moving a positive test charge between two points in an electric field. ∆V = W/q (W is the work done on moving the charge; q is the magnitude of the charge being moved). ∆V is measured in J/C or volts (V). fields/charges-and-fields_en.html fields/charges-and-fields_en.html

Sample Problem If a 12 V battery does 1200 J of work transferring charge, how much charge is transferred? ∆V = W/q 12 = 1200/q q = 100 C

Electric Potential in a Uniform Field A uniform field can be made by placing two large, flat, conducting plates parallel to each other. One is charged positively and the other is charged negatively. The electric field between the plates is constant and work is done if the charge is moved in the direction opposite the electric field direction. ∆V = W/q = Fd/q = (F/q)d = Ed

Sample Problem A voltmeter indicates that the electric potential difference between two plates is 70.0 V. The plates are m apart. What electric field intensity exists between them? ∆V = Ed 70.0 = E(0.020) E= 3500 N/C

Application: Millikan’s Oil Drop Experiment In a Millikan Oil Drop Experiment, a drop has been found to weigh 2.4 x N. The parallel plates are separated by a distance of 1.2 cm. When the potential difference between the plates is 450 V, the drop is suspended, motionless. What is the charge on the oil drop? ∆V = Ed 450 = E(.012) E = 37, 500 N/C E = F/q 37, 500 = 2.4 x N/q q = 6.4 x C

Application: Millikan’s Oil Drop Experiment How many excess electrons are on the oil drop? 1 electron = 1.6 x C q = 6.4 x C 6.4 x /1.6 x = # of electrons # of electrons = 4

Capacitors A capacitor is a device used for storing charge. Capacitors store energy is the form of separated charges. All capacitors are made up of two conductors that are separated by an insulator. The two conductors have equal and opposite charges. Capacitors are used in electric circuits to store charge. A lightning storm acts as a giant capacitor arrangement (The cloud is one charged plate and the Earth is the other. The air acts as the insulator)

Capacitors C = q/∆V (q is the net charge on each plate; ∆V is the stored energy obtained by the work done in separating the charges). The unit for capacitance is the C/V or the farad, F.

Discharging a Capacitor When plates of a capacitor are connected to a conductor, it will discharge. Charges move back to region of lowest potential energy. Example: flash in a camera