Electric Field Lines Drawing electric field lines Motion of charged particles in an electric field Electric flux

Electric Field Lines Electric field lines are a way of visualizing the field. Rules for Drawing field lines: 1)Lines start on (+) charges, end on (-) charges, or go to infinity 2)(# of lines)  charge 3)Lines never cross 4)Strength of field is proportional to the density of field lines Interpreting the picture: is parallel to the field line at each point.

Electric Field lines for an isolated Charge +Q + E – magnitude of field E E Q

Field lines + Area S, Where is the density of field lines greatest?

2 Point Charges -2Q +Q Note: number of lines on -2Q is twice as many as on +Q

Quiz: -q qq Which way will the dipole start to move in the electric field? A)up B)down C)left D)right E)nowhere – there is no net force.

Quiz: -q qq Does this dipole feel a torque ? A)Yes - clockwise B)Yes – counter clockwise C)No D)Depends on the strength of E

Parallel Charged Plates E approx. uniform, between the plates, except near the edges.

Electric Force Therefore we can solve for motion as easily as projectile motion!

Example: Uniform E 0.1m - An electron enters a uniform field of E = -200N/C j with an initial velocity of v o = 3x10 6 m/s i. Find: a) The acceleration of the electron b) The time it takes to travel through the region of the field c) The vertical displacement of the electron while in the field

Solution:

Electric Flux Electric flux is the measure of the “number of field lines passing through a surface S ” For uniform : Define: Electric Flux S Units: Nm 2 /C A is the surface area perpendicular to S, so Φ=EAcos(θ)

Notes: 1) is a scalar called electric flux 2)Units: Nm 2 /C 3) represents the “number of field lines through surface S.” 4)For a closed surface, the area vector points in the outward direction. 5) Flux is zero for a surface parallel to the field (normal is at 90 o to E)

Example: Find: flux through S 1, S 2, S 3. 30° (rectangle, 1m x 2m) (rectangle, 1m x 2m) (hemisphere, radius 1m) S2S2 S1S1 S3S3

solution

If E is not uniform, or S is not flat, then: For a small surface For the whole surface,

Summary Electric field lines help show the direction of E Electric flux is defined as the magnitude of the field times the area (maybe negative if the angle between the vectors is more than 90 degrees) Electric flux is a quantitative equivalent to “the number of field lines through a surface”.