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Electric Field
• Take a small positive test charge q0 at some point in space P.
• Find the force produced on it by all of the other charges in the system.
• Each of those forces proportional to q0.
• So total force is proportional to q0.
• Electric field is total force divided by q0.
0
0
P qq
F
E = F E
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The direction of the electric field at a point is the same as
1) the direction of the force on a neutron placed at that point.
2) the direction of the force on a proton placed at that point.
3) the direction of the force on an electron placed at that point.
4) the direction of the force on a hydrogen molecule placed at that point.
5) None of these is correct.
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Electric field of single point charge
,2,
ˆP q P
q P
kq
rE = r
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Electric field of single point charge –2D view
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Electric field of single point charge –3D view
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More than one point charge
• Electric fields add like vectors (Principle of Superposition).
• The total electric field at point P is the vector sum of the fields due to each of the individual point charges.
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Electric Dipole
• Two equal, but opposite charges a fixed distance apart.
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Electric field produced by a dipole
• Along x axis:
• Electric “dipole moment”:
Points in direction – to +.
)(or for ˆ12
ˆ2
3
222
axaxx
kql
ax
xkql
i
iE
qlp
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Dipole electric field – 2D view
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Dipole electric field – 2D view
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Electric Field Lines
• Field lines start or end at charges or at infinity.
– Lines are directed outwards from positive charges and inward towards negative charges.
– # of lines starting or ending at a charge is proportional to the magnitude of that charge (constant of proportionality is arbitrary, i.e. up to you).
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Electric Field Lines
• Relation to Electric Field
– The Electric Field points along the tangent of the field lines. Charges do not in general move along the field lines!
– The magnitude of the Electric Field is proportional to the density of field lines.
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The figure shows the field lines for two charges. What might be the ratio of the left
charge to the right charge?
1) 1:2
2) 1:2
3) 2:1
4) 2:1
5) 2:1