# EXAM PHYSICS CSULA MIDTERM PHYSICS 213 Spring

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```					              CSULA                               MIDTERM                            PHYSICS 213
Spring 2008
Professor: Rafael Obregon

Name (Last, First): _________________________________________________

I.      CONCEPTUAL QUESTIONS (5 points ea): Answer these in a few complete and grammatically
correct English sentences. Note that a correct explanation will be worth 4 points and merely
choosing the correct answer will be worth 1 point.

1. A test charge of +3C is at a point P where an external electric field is directed to the right
and has a magnitude of 4106 N/C. If the test charge is replaced by another test charge of
–3C the external electric field at P: (a) Is the same. (b) Has opposite direction. (c)
Increases. (d) Decreases. (e) Changes but we need to know the force also.
Explain. (Sketching a diagram may be a good help)

2. Suppose a point charge (+ q) is located at the center of a spherical surface. The electric
field at the surface of the sphere and the total flux through the sphere are determined. Now
the radius of the sphere is doubled. What happens to the flux through the sphere and the
magnitude of the electric field at the surface? (a) The flux and the field both increases. (b)
The flux and the field both decreases. (c) The flux increases, and the field decreases. (d)
The flux decreases, and the field increases. (e) The flux remains the same, and the field
increases. (f) The flux remains the same, and the field decreases. (g) The flux decreases,
and the field remains the same. Explain your answer using some related formula.

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3. The closed Gaussian surface shown in the figure consists of a hemispherical surface and a
flat plane. A point charge + q is outside the surface, and no charge is enclosed by the
surface.
A. What is the net flux through the entire closed surface?

B. Let L represents the flux through the flat left-hand portion of the surface. Using the
result from part A, write an expression in terms of L for the flux (C ) through the
curved surface.

4. In class we show that the electric field (at any distance) due
to an infinite plane of positive charge with uniform surface
charge density  is equal to:  / 2 o  .
If we place two infinite planes positive charged such that
they are parallel to each other, what is the magnitude of the
electric field between and outside of the two planes?
Explain using direction of the electric field.

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II) Solve

1. (20 pts) Consider the electric dipole shown in the
figure.

A. Find an expression for the electric field at
any point on the +x axis (to the right of – q).

B. What is the electric field if x >> a ?

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2. (20 pts) A Wire having a uniform linear charge density (λ) is bent into the shape shown in the
figure. Show that the electric potential at point O is given by: k e    2 ln 3
(Hint: Use three integrals, taking O as the origin of your Cartesian coordinates)

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3. (20 pts) An insulating solid sphere of radius a has a uniform
volume charge density  and carries a total positive charge
Q (see the figure). Using Gauss’s Law, calculate the
magnitude of the electric field at a point r > a.

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4. (20pts) For the uniformly charged ring of radius a an total
charge Q (see the figure):

A. Find an expression for the electric potential at a point P
located on the perpendicular central axis of the ring.

B. Using the result from part A find an expression for the magnitude of the electric field at point
P.

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