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PSC #29 Electric and Gravitational Forces and Fields

= 8.85 × 10⁻¹² F/m (F/m - Farads/meter)

mass of electron = 9.11×10^-31 kg

1) Two point charges, q_a = 50.0 µC and q_b = 100 µC, are separated by a distance d = 1.00 m.

a) What is the electric field at a point halfway between the charges?

b) What force would be exerted on a third charge q_a = 20.0 µC placed at this point?

2) Two equal positive charges, q ₁ = q ₂ = 2.00 µC are situated at a distance l apart as shown. A point A is situated such that the angle “ q ₁A q _2” is a right angle. The distances r ₁ = 0.819 m, r ₂ = 0.574 m. Find the resultant electric field intensity at A.

A

r₁ r₂

q₁ q₂

l

3) Three point charges lie along the x-axis. The charge q₁ = +15.0 µC is at x = 2.00 m,

the charge q₂= +6.00 µC is at the origin, and the resultant force acting on q₃ is

zero. What is the x-coordinate of q₃?

4) An electron moving horizontally with speed, v_o= 3.00 × 10⁶ m/s, enters the region of a uniform electric field, E = 200 N/C. The horizontal length of the plates is 0.100 m.

a) Find the acceleration of the electron while it is in the electric field.

b) Find the time it takes the electron to travel through the field.

c) What is the vertical displacement y of the electron while it is in the field?

e^-

5) A uniformly charged insulating rod of length 10.0 cm is bent into the shape of a semicircle. The total charge on the rod is 5.00 µC. Find the magnitude and direction of the electric field at the centre of the semicircle (point x). (Hint: think integration)

6) Two small metallic spheres, each of mass 0.200 g are suspended as pendulums by light strings from a common point as shown in the figure. The spheres are given the same electric charge and it is found that they come to equilibrium when each string is at an angle of 5.00° with the vertical. If each string is 30.0 cm long, what is the magnitude of the charge on each sphere?

𝞱

7) *A total amount of charge Q is uniformly distributed along a thin, straight, plastic rod of length L. (see Figure).

a) Find the electric force acting on a point charge q located at point P, at a distance d from one end of the rod.

b) Find the electric force acting on a point charge q located at point P', at a distance y from the midpoint of the rod.

P’

y

L d p