The Electric Field Figure 21-22. Force exerted by charge Q on a small test charge, q, placed at points A, B, and C.

The Electric Field: Introduction The Electric Force is a Field Force. Field forces can act through all space. Their effects are produced even with no physical contact between objects. Faraday developed the concept of a force in terms electric fields. Figure 21-22. Force exerted by charge Q on a small test charge, q, placed at points A, B, and C.

The Electric Field  The direction of the Electric Field due The Electric Field is defined as the force on a small positive charge q, (a “Test Charge”) divided by the magnitude of the charge:  Figure 21-22. Force exerted by charge Q on a small test charge, q, placed at points A, B, and C. The direction of the Electric Field due to a positive charge +Q is radially outward from the charge.

 The direction of the Electric Field due to a positive charge +Q is radially outward from the charge. Figure 21-22. Force exerted by charge Q on a small test charge, q, placed at points A, B, and C.

An Electric Field surrounds every charge. An Electric Field exists in the region of space around a charged object. This charged object is the Source Charge, When another charged object, the Test Charge, enters this electric field, an electric force acts on it. Figure 21-21. An electric field surrounds every charge. P is an arbitrary point.

In terms of ε0,the permittivity of free space: The Electric Field due to a single point charge Q is: In terms of ε0,the permittivity of free space:

The direction of E is that of the force on a positive test charge. We can also say that an electric field exists at a point if a test charge at that point experiences an electric force. The SI units of E are N/C (or V/m).

This is valid for a point charge only. If q is negative, The Force on a positive point charge q in an electric field E: Electric Field E Force F on a positive point charge q. This is valid for a point charge only. If q is negative, the Force F & the Electric Field E point in the opposite direction than when q is positive. Figure 21-23. (a) Electric field at a given point in space. (b) Force on a positive charge at that point. (c) Force on a negative charge at that point. Force F on a negative point charge -q.

Electric Field, Vector Form Remember that Coulomb’s Law, between the source & test charges is Then, the electric field will be Figure 21-23. (a) Electric field at a given point in space. (b) Force on a positive charge at that point. (c) Force on a negative charge at that point.

More On Electric Field Direction If a Charge q is Positive, the Force is Directed Away from q. (Fig. a) The Electric Field Direction is Also Away from a Positive Source Charge. (Fig. b) Figure 21-23. (a) Electric field at a given point in space. (b) Force on a positive charge at that point. (c) Force on a negative charge at that point.

Also Towards a Negative Source Charge. If a Charge q is Negative, the Force is Directed Towards q. (Fig. c) The Electric Field Direction is Also Towards a Negative Source Charge. (Fig. b) Figure 21-23. (a) Electric field at a given point in space. (b) Force on a positive charge at that point. (c) Force on a negative charge at that point.

Electric Fields from Multiple Charges At any point P, the total electric field E due to a group of source charges qi equals The Vector Sum of the electric fields of all of the charges: Figure 21-23. (a) Electric field at a given point in space. (b) Force on a positive charge at that point. (c) Force on a negative charge at that point.

Electric Forces & Electric Fields Problem Solving in Electrostatics: Electric Forces & Electric Fields Sketch a Diagram showing all charges, with signs, & electric fields & forces with directions. Calculate Forces using Coulomb’s Law. Add Forces Vectorially to get the result. Check Your Answer!

Field Lines The electric field is stronger where the field lines are The electric field can be represented by field lines. These lines start on a positive charge & end on a negative charge. The number of field lines Starting (ending) on a positive (negative) charge is proportional to the magnitude of the charge. The electric field is stronger where the field lines are closer together.

2 equal charges, opposite in sign: Electric Dipole: 2 equal charges, opposite in sign:

The electric field between two closely spaced, oppositely charged parallel plates is constant.

Summary of Field Lines: Field lines indicate the direction of the field; the field is tangent to the line. The magnitude of the field is proportional to the density of the lines. Field lines start on positive charges & end on negative charges; the number is proportional to the magnitude of the charge.

Electric Fields and Conductors (Electrostatics) The static electric field inside a conductor is zero – if it were not, the charges would move. So, the net charge on a conductor is on its surface (under static conditions)

Under static conditions, the electric field is perpendicular to the surface of a conductor. Again, if it were not, the charges would move.