4/1/16Oregon State University PH 213, Class #31 Force Fields “Action at a distance” (across “empty” space)—how is this possible? This happens with gravitational force and it happens with electrical force. Newton wrestled with this question and never resolved it—because he thought only of a material connection (i.e. some bit of matter) acting as the agent of the force. But obviously force and energy can be transmitted across a complete vacuum (outer space)! This led physicists over the 150 years after Newton to accept the idea that space itself has properties. A field is a point-by-point description of some property of space itself. A force field, for example, describes the magnitude and direction of the force that will be exerted on a body when it is placed at a given point in that space.

4/1/16Oregon State University PH 213, Class #32 Even when considering force fields, the parallels remain between gravitational and electrostatic forces: The gravitational force, F G, on a body of mass, m, located at a point P, is given by F G = mg, where g is the gravitational force field at point P: g = –Gm P /r 12 2 r In other words, g is the property of that point P in space; and m is the property of the body placed there. Notice that F G and g are vectors here; they have magnitudes and directions. If we know m and g, we can compute F G. Or, if we know m and F G, we can find g. … Example: A brick of mass 3.0 kg weighs 6.0 N on the moon’s surface. Find the magnitude and direction of the gravitational field on the lunar surface (expressed in x-y axes).

4/1/16Oregon State University PH 213, Class #33 Likewise, the electrostatic force, F E, on a body with net charge, q, located at a point P, is given by F E = qE, where E is the electric force field—at point P. In other words, E is the property of that point P in space; and q is the property of the body placed there. Notice the units of E.… F E and E are vectors—with magnitudes and directions. If we know q and E, we can compute F E ; if we know q and F E, we can find E.…

4/1/16Oregon State University PH 213, Class #34 Example: An electrostatic force of 6.0 N is acting on a point charge of 3.0  C. Calculate the magnitude and direction of the electric field, E, that must be present at the location of the charge. Again, the analogy: To find the gravitational force, F G, on an object, we must know its mass, m, and the gravitational force field, g, at its location. To find the electrical force, F G, on an object, we must know its charge, q, and the electrical force field, E, at its location.

4/1/16Oregon State University PH 213, Class #35 The Force and the Field Coulomb’s Law gives the magnitude of the electrostatic force between two point charges:  F E  = k  q  q   /r 2. But we now know we can also express F E as the product of the charge that feels that force and a property of a point in space—the vector quantity that we call the electric field at that point. For example, the force magnitude felt by q 0 (exerted by q) would be  F E  = q 0  E . Thus, k  q  q 0  /r 2 = q 0  E , or in other words:  E  = k  q  /r 2 This is the magnitude of the electric field, E, that is caused by q and felt by q 0. Note: A charge does not feel the E-field it causes (just as a mass does not feel its own gravity).

4/1/166Oregon State University PH 213, Class #3

4/1/16Oregon State University PH 213, Class #37 Notice: E-fields help us use the signs of the charges to indicate the directions of the forces they feel. E-field lines begin at (point away from) a positive point charge. E-field lines terminate (point toward) a negative point charge. Using F E = q 0 E (full vector notation now), we can easily decide the direction of the force felt by any charge q 0 placed into that field: If a positive charge, q 0, is placed into an E-field, it feels a force in the same direction as the E-field lines at that point. If a negative charge, q 0, is placed into an E-field, it feels a force in the direction opposite to the E-field lines at that point.

More examples: What is the strength and direction of the electric field 1 nm from a proton? What force would an electron feel if placed in the field of that proton 1 nm away? 4/1/168Oregon State University PH 213, Class #3

4/1/16Oregon State University PH 213, Class #39 Notice, too: The total E-field at a given point is the vector sum of the fields caused by individual point charges. This principle of superposition is fundamental to understanding fields and using them conveniently.

Consider the four field patterns. Which pattern(s) could represent a field caused by one or a few fixed point charges? 1.(a) 2.(b) 3.(b) and (d) 4.(a) and (c) 5.(b) and (c) 6.Some other combination 4/1/1610Oregon State University PH 213, Class #3

A. Up. B. Down. C. Left. D. Right. E. The electric field is zero. Assuming all charges have equal magnitude, at the position of the dot, the electric field points… 4/1/1611Oregon State University PH 213, Class #3

4/1/16Oregon State University PH 213, Class #312 Example: Point charge A (q A = +2e) sits at x = 0. Point charge B (q B = +8e) sits at x = 3. Find the total E-field magnitude produced by the charges at the point x = 2 (all distances in µm). (How about at x = 1?)

4/1/16Oregon State University PH 213, Class #313 E-Field Models There are several E-field situations or models that we’ll study. One model is the net (total) field produced by one or more discrete point charges (which are the examples we’ve worked with so far). The other, more general, models are the net (total) fields produced by a variety of continuous charge distributions.