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Physics 1302.200 Spring 2015 Class 4—January 27, 2015 Main Topics: • Electric Field Representa5on of Fields •  Here are examples of an arrow map and a lines of force map. •  Field lines start and end on charge. Physics 1301.200 Fall 2014 2 Ques5on •  Which of the following choices best describes the field
lines around a single positive charge? [Remember that
like charges repel and field lines point in the direction of
motion of a positive test charge.]
–  (a) Field lines point radially outward
–  (b) Field lines point radially inward
–  (c) Field lines form concentric circles around the charge, pointing
counterclockwise
–  (d) Field lines form concentric circles around the charge, pointing
clockwise
–  (e) Field lines spiral around the charge
Physics 1301.200 Fall 2014 3 Electric Field •  The electric field is linear, so you can calculate the field for mul5ple charges by calcula5ng the fields for individual charges and adding the fields together as vectors. •  The electric field does not depend on the test charge q. •  The force at any point is a par5cular charge 5mes the electric field at that point. Physics 1301.200 Fall 2014 q1
E = k 2ˆ
r
r
n
X
qi
E=k
rˆi
2
r
i=1 i
Z
⇢
E=k
ˆ
rdV
2
r
F = qE
4 Electric Fields •  The electric field of a point charge. Physics 1301.200 Fall 2014 5 Electric Fields •  The electric field of a dipole. Physics 1301.200 Fall 2014 6 Ques5on Physics 1301.200 Fall 2014 7 Ques5on •  Which electric field is responsible for the proton’s trajectory? Physics 1301.200 Fall 2014 8 Vector Calculus of Electric Fields •  Electric field lines point outward from posi5ve charge; inward towards nega5ve charge. •  The divergence div E of the electric field is posi5ve at posi5ve charge and nega5ve at nega5ve charge. •  In electrosta5cs, curl E is zero. Physics 1301.200 Fall 2014 Divergence ∇ ⋅ E
Curl ∇ × E
Cartesian Coordinates:
∂ ˆ ∂ ˆ ∂ ˆ
∇=
i+
j+ k
∂x
∂y
∂z
9 Ques5on •  Consider the four field paNerns shown. Assuming there are no charges in the regions shown, which of the paNerns represent(s) a possible electrosta5c field? (a) (a) (b) (b) (c) (b) and (d) (d) (a) and (c) (e) (b) and (c) Physics 1301.200 Fall 2014 10 Ques5on •  An electron ini5ally moving horizontally near Earth’s surface enters a uniform electric field and is deflected upward. What can you say about the direc5on of the electric field (assuming no other interac5on such as gravity)? (a) The electric field points upward. (b) The electric field points downward. (c) The electric field has an upward component. (d) The electric field has a downward component. (e) There is not enough informa5on to tell. Physics 1301.200 Fall 2014 11 Cathode Ray Tube (CRT) •  The most important elements of a Cathode Ray Tube (CRT) are: –  A vacuum vessel (usually glass). –  A hot cathode that releases electrons by thermionic emission. –  An accelera5ng anode. –  X and Y deflec5on plates that use electric fields to steer the electron beam. –  A fluorescent screen. Physics 1301.200 Fall 2014 12 Ques5on The electric charge per unit area is +σ for plate 1 and –σ for plate 2. The magnitude of the electric field associated with plate 1 is σ/2eo, and the electric field lines for this plate are as shown. When the two are placed parallel to one another, the magnitude of the electric field is • 
• 
• 
• 
• 
(a) σ/eo between, 0 outside. (b) σ/eo between, kσ/eo outside. (c) Zero both between and outside. (d) kσ/eo both between and outside. (e) none of the above. Physics 1301.200 Fall 2014 13