y +) d d Consider four positive charges with charge Q arranged in a square with side-length d, centred about the origin in the r – y plane, as shown in the figure above. (a) Sketch the electric field of the charge configuration, using field lines. Describe how you constructed your sketch, and list some key features of charges and electric field lines that your sketch demonstrates. You could use the above figure as the basis of your sketch, or start from blank paper. (b) Derive an expression for the electric potential V(r, y) in the r – y plane. (c) Describe, using concepts and terminology used in PHYS1002, the difference between electric potential and potential energy.
y +) d d Consider four positive charges with charge Q arranged in a square with side-length d, centred about the origin in the r – y plane, as shown in the figure above. (a) Sketch the electric field of the charge configuration, using field lines. Describe how you constructed your sketch, and list some key features of charges and electric field lines that your sketch demonstrates. You could use the above figure as the basis of your sketch, or start from blank paper. (b) Derive an expression for the electric potential V(r, y) in the r – y plane. (c) Describe, using concepts and terminology used in PHYS1002, the difference between electric potential and potential energy.
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Transcribed Image Text:d
+)
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d
Consider four positive charges with charge Q arranged in a square with side-length d, centred about the origin
in the r - y plane, as shown in the figure above.
(a) Sketch the electric field of the charge configuration, using field lines. Describe how you constructed your
sketch, and list some key features of charges and electric field lines that your sketch demonstrates. You
could use the above figure as the basis of your sketch, or start from blank paper.
(b) Derive an expression for the electric potential V(r, y) in the r- y plane.
(c) Describe, using concepts and terminology used in PHYS1002, the difference between electric potential and
potential energy.
(d) Derive an expression for the potential energy U of the charge configuration, and show that it is given by
U =
(4 + v2) Q²
· P
(e) The charges are all released simultaneously from rest, and accelerate away from each other due to Coulomb
repulsion. If Q = 22.4 µC, d = 1.50 mm and the mass of each is 1.00 g, calculate their speed when they
are very far apart. Include appropriate significant figures in your answer.
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