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: Lines start on (+) charges, end on (-) charges, or go to infinity (# of lines)  charge Lines never cross 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 E – magnitude of field E + Q

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

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

Quiz: Which way will the dipole start to move in the electric field? up down left right nowhere – there is no net force.

Quiz: Does this dipole feel a torque ? Yes - clockwise Yes – counter clockwise No 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 An electron enters a uniform field of E = 200N/C j with an initial velocity of vo = 3x106 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 0.1m -

Solution:

Electric Flux Electric flux is the measure of the “number of field lines passing through a surface S ” For uniform : Define: Electric Flux Units: N•m2/C S A is the surface area perpendicular to , so Φ=EAcos(θ)

Notes: is a scalar called electric flux Units: N•m2/C represents the “number of field lines through surface S.” 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 90o to E)

Example: (rectangle, 1m x 2m) (hemisphere, radius 1m) S2 S1 S3 30° (rectangle, 1m x 2m) (hemisphere, radius 1m) S2 S1 S3 Find: flux through S1, S2, S3.

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”.