16 – 3 Electric Field

The Electric Field Both the gravitational and electrostatic force act through space, involving no contact between the objects involved. In order to describe the interaction process under these forces, a concept of a field was introduced.

An electric field is said to exist in the region of space around a charged object. When another charged object enters this electric field, the field exerts a force on the second object.

The Electric Field Consider a small charge q0 near a larger charge Q. We define the electric field E at the location of the small test charge as a ratio of the electric force F acting on it and the test charge q0

The Electric Field Magnitude of an electric field SI Unit = N/C Note: This is the field produced by the charge Q, not by the charge q0!

ELECTRIC FIELD +Q FORCE FORCE -Q The direction of E at a point is the direction of the electric force that would be exerted on a small positive test charge placed at that point.

The Electric Field Due to a Point Charge The force on a charge q0 placed at some point in the field due to another charge is given by: |Q| |q0| F = ke  r2 |Q| E = ke  r2 since E = F / q0 This is the electric field due to a charge Q. If Q is positive, then the field is radially outward from it. If Q is negative, then the field is radially toward it.

Visualizing the Electric Field Electric field lines are used to represent the magnitude and direction of the electric field. Field lines originate on positive charge, or at infinity and terminate on negative charge or at infinity The electric field vector is tangent to the electric field lines at each point. The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region. No two field lines can cross each other.

Visualizing the Electric Field

Electrostatic Equilibrium In conductors the electrons are free to move within the material. When no net motion occurs within a conductor, it is said to be in electrostatic equilibrium. Properties of an isolated conductor: All of the charge resides at the surface E = 0 inside the conductor The electric field just outside the conductor is perpendicular to the surface On an irregularly shaped conductor charge accumulates at sharp points

Sample Problem A charge of q1 = 4.50 C experiences an attractive force of 1.35 N at a distance of 15.0 cm from a charged object q2. Find the strength of the electric field due to q2 at this distance. Find the charge on q2. Given: q1 = 4.50 mC F = 1.35 N r = 0.15 m E = ?

By Newton’s 3rd law the force on charge 2 equals the force on charge 1 so,