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Exam 1

11 February 2008

Name_____________________

Coulomb’s constant: k=9x10

9

N

⋅ m

2

/C

2

1) (20 pts) The charges and coordinates of two charged particles held fixed in an xy plane are q

1

=+5.0 nC, x

1

=3.0 cm, y

1

=0.75 cm and q

2

=-3.0 nC, x

2

=-1.5 cm, y

2

=1.5cm. Find (a) magnitude and (b) direction of the electrostatic force on particle one due to particle two.

At what (c) x- and (d) y-coordinates should a third particle of charge q

3

=+4.0 nC be placed such that the net electrostatic force on particle 3 due to particles 1 and 2 is zero? a.

Magnitude of F b.

c.

d.

Direction of F

X-coordinate

Y-coordinate

2) (20 pts) In this figure, the four particles are fixed in place as shown. The charges are q

1

=3 nC, q

2

=-10 nC, q

3

=2 nC, and q

4

=-3 nC. The distance d is 0.1m (d=0.1 m). What is the net electric field, in unit-vector notation, at point P?

What is the force, in unit vector notation, on a 1µC charge placed at point P?

3) (15 pts) A non-conducting spherical shell, with an inner radius of 2.0 cm and an outer radius of 6.0 cm, has charge spread nonuniformly through its volume between its inner and outer surfaces. The volume charge density is the charge per unit volume

(C/m

3

). For this shell, ρ=b/r

2

where b=2.0 µC/m. What is the net charge on the shell?

4) (10 pts)Sketch qualitatively the electric field lines both between and outside two concentric conducting spherical shells when a uniform positive charge +q

1

is on the inner shell and a uniform negative charge -q

2

is on the outer. Consider the cases q

1

= q

2

, q

1

> q

2

, and q

1

< q

2

.

5) (20 pts) (a) What is the electric field in vector notation at the point (2.0 i + 3.0 j - 4.0 k) meters if the electric potential is given by V

=

2.0

2

, where V is in volts and x, y, and z are in meters?

(b) What is the magnitude of the electric field?

6) (15 pts)In this figure, what is the net electric potential at point P due to the four particles if V=0 at infinity and d=0.1 m? The charges are: q

1

=3 nC, q

2

=-10 nC, q

3

=2 nC, and q

4

=-3 nC.