Physics tutorial #13

1. If we launch an electron into the uniform electric field ~

E with an initial horizontal velocity ~

v

0

, what

is the equation of its trajectory, y(x) =? ( ~

E is vertical, perpendicular to ~

v

0

; neglect gravity)

2. Two equal point masses with equal positive charges q = 1µC each are separated by the distance

x = 10 cm. What is the value of these masses such that the net force (gravity force + electric force)
acting on each mass is zero? Assume that there are no external fields (gravitational, electric etc.).

3. Point charges q

1

and q

2

of +12 nC and −12 nC, respectively, are placed 0.10 m apart. Compute the

electric field at the three points, placed: (a) 6 cm from q

1

and 4 cm from q

2

, (b) 4 cm from q

1

and

14 cm from q

2

, (c) 13 cm from q

1

and 13 cm from q

2

.

4. Determine the point on the line joining two charges q

1

and q

2

placed a distance l apart at which the

electric field is zero.

5. A charged cork ball of mass m = 1 g is suspended on a light string in the presence of a uniform

electric field. When ~

E = (3ˆ

x + 5ˆ

y) × 10

5

N/C, the ball is in equilibrium and the angle between the

string and the vertical is θ = 37

◦

. Find the charge on the ball and the tension in the string.

6. Show that the potential energy for a dipole in an electric field equals U = −~

p · ~

E.

7. A thin ring-shaped conductor with radius a carries a total charge Q uniformly distributed around

it. (a) Show that the electric field at a point P that lies on the axis of the ring at a distance x from
its centre is equal E =

kQx

(x

2

+a

2

)

3/2

. (b) What is the approximate result if x  a?

8. Positive electric charge Q is distributed uniformly along a line with length 2a, lying along the y-axis

between y = −a and y = +a. (a) Find the electric field at a point P on the x-axis at a distance x
from the origin. (b) Find the result if a → +∞, with the charge per unit length equal λ.

9. (a) Find the electric field caused by a disk of radius R with a uniform positive surface charge density

(charge per unit area) σ, at a point along the axis of the disk a distance x from its centre. Assume
that x is positive. (b) Find the result in case of an infinite disk starting from the result obtained
here and than using the Gauss’s Law. (c) What is the electric field produced by two infinite plane
sheets placed parallel to each other, separated by a distance d? One of them has a uniform charge
density +σ, and the other −σ.

10. (Gauss’s Law) (a) We place positive charge q an a solid conducting sphere with radius R. Find

~

E at any point inside or outside the sphere. (b) Electric charge is distributed uniformly along a
infinitely long, thin wire. The charge per unit length is λ (assumed positive). Find the electric
field. (c) Positive charge is distributed uniformly throughout the volume of an insulating sphere
with radius R. Find the magnitude of the electric field at a point P a distance r from the centre of
the sphere (0 < r < +∞).

Nivas Babu Selvaraj, Maciej Wo loszyn
http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/