Physics 2113 Lecture 13 - Louisiana State University
Transcript of Physics 2113 Lecture 13 - Louisiana State University
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Physics 2113 Lecture 13
EXAM I: REVIEW
Physics 2113 Jonathan Dowling
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A few concepts: electric force, field and potential
• Gravitational Force – What is the force on a mass produced by other masses? – Kepler’s Laws & Circular Motion
• Gravitational Potential Energy • – Conservation of Energy • Electric force:
– What is the force on a charge produced by other charges? – What is the force on a charge when immersed in an
electric field? • Electric field:
– What is the electric field produced by a system of charges? (Several point charges, or a continuous distribution)
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Plus a few other items… • Electric field lines
• Electric dipoles: field and potential produced BY a dipole, torque ON a dipole by an electric field, torque and potential energy of a dipole
• Gauss’s Law: For conductors, planar symmetry, cylindrical symmetry, spherical symmetry. Return of the Shell Theorems!
�What? The Flux! Φ=q/ε0 . Given the field, what is the charge enclosed? Given the charges, what is the flux? Use it to deduce formulas for electric field.
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Conservation of Mechanical Energy!
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Conservation of Mechanical Energy!
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Charged Insulators & Conductors
• Will two charged objects attract or repel?
• Can a charged object attract or repel an uncharged object?
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Electric forces and fields: point charges
Figure 22N-14 shows an arrangement of four charged particles, with angle q = 34° and distance d = 2.20 cm. The two negatively charged particles on the y axis are electrons that are fixed in place; the particle at the right has a charge q2 = +5e
(a) Find distance D such that the net force on the particle at the left, due to the three other particles, is zero.
(b) If the two electrons were moved further from the x axis, would the required value of D be greater than, less than, or the same as in part (a)?
Other possible questions: what’s the electric field produced by the charges XXX at point PPP ? what’s the electric potential produced by the charges XXX at point PPP ? What’s the potential energy of this system?
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Electric dipoles
• What’s the electric field at the center of the dipole? On axis? On the bisector? far away?
• What is the force on a dipole in a uniform field?
• What is the torque on a dipole in a uniform field?
• What is the potential energy of a dipole in a uniform field?
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Electric fields of distributed charges
Possible problems, questions: • What’s the electric field at the center of a charged circle? • What’s the electric field at the center of ¼ of a charged circle? • What’s the electric field far from the ring? far from the disk? • What’s the DIRECTION of an electric field of an infinite disk?
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Exam Review Continued • Questions: from checkpoints and
questions in the textbook!
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Problem
• Calculate electric field at point P.
P x
L a dx
E
• Field very far away?
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Problem
Field at center of arc?
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Line Of Charge: Field on bisector
Distance 22 xad +=
2)(
ddqkdE =
Lq=λCharge per unit length
2/322 )()(cos
xaadxkdEdEy +
== λθQ
L
a
P
o x
dE
θ
dx
d
2/122 )(cos
xaa
+=θ
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Line Of Charge: Field on bisector ∫
− +=
2/
2/2/322 )(
L
Ly xa
dxakE λ
What is E very far away from the line (L<<a)?
2242
LaaLk+
= λ
2/
2/222
L
Laxa
xak−⎥⎦
⎤⎢⎣
⎡
+= λ
ak
LaLkEy
λλ 222==
Ey~2klL/a(2a)=klL/a2=kq/a2
What is E if the line is infinitely long (L >> a)?
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Electric fields: Example Calculate the magnitude and direction of the electric field produced by a ring of charge Q and radius R, at a distance z on its axis.
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Sample Problem Figure 22N-14 shows an arrangement of four charged particles, with angle q = 34° and distance d = 2.20 cm. The two negatively charged particles on the y axis are electrons that are fixed in place; the particle at the right has a charge q2 = +5e
(a) Find distance D such that the net force on the particle at the left, due to the three other particles, is zero.
(b) If the two electrons were moved further from the x axis, would the required value of D be greater than, less than, or the same as in part (a)?
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At each point on the surface of the cube shown in Fig. 24-26, the electric field is in the z direction. The length of each edge of the cube is 2.3 m. On the top surface of the cube E = -38 k N/C, and on the bottom face of the cube E = +11 k N/C. Determine the net charge contained within the cube. [-2.29e-09] C
Gauss’ law
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Gauss’s Law: Cylinder, Plane, Sphere
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Problem: Gauss’ Law to Find E
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Two Insulating Sheets
ER = EL
σ + = +Q+ / A σ − = −Q− / A
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Two Conducting Sheets
ER = E− ≠ EL
4.86
7.68 12.54
E does not pass through a conductor Formula for E different by Factor of 2
7.68
4.86
σ + = + 12Q+ / A
σ − = − 12Q− / A
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Electric Fields With Insulating Sphere r < R
qins =QVinsVtotal
⎛⎝⎜
⎞⎠⎟=Q 4πr3 / 3
4πR3 / 3⎛⎝⎜
⎞⎠⎟=Q r3
R3
r > Rqins =Q
Φ = EA = qins / ε0
r < R→ E4πr2 = Q r3
R3/ ε0
r > R→ E4πr2 = Q / ε0
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