1. Three point charges are placed on the x-axis. A charge of +2.0 µC is placed a

Question

1. Three point charges are placed on the x-axis. A charge of +2.0 µC is placed at the origin, -2.0 µC to the right at x = 50 cm, and +4.0 µC at the 100 cm mark. What are the magnitude and direction of the electric force that acts on the charge at the origin?
  
2. Three +3.0-µC point charges are at the three corners of a square of side 0.50 m. The last corner is occupied by a -3.0-µC charge. Find the magnitude of the electric field at the center of the square.

3. An electric field of magnitude 3.50 kN/C is applied along the x axis. Calculate the electric flux through a rectangular plane 0.350 m wide and 0.700 m long (a) if the plane is parallel to the yz plane, (b) if the plane is parallel to the xy plane, and (c) if the plane contains the y axis and its normal makes an angle of 40.0° with the x axis.

4. Consider a thin, spherical shell of radius 14.0 cm with a total charge of 32.0 mC distributed uniformly on its surface. Find the electric field at (a) 10.0 cm and (b) 20.0 cm from the center of the charge distribution.

5. Two equally charged tiny spheres of mass 1.0 g are placed 2.0 cm apart. When released, they begin to accelerate away from each other at 414 m/s2 . What is the magnitude of the charge on each sphere, assuming only that the electric force is present?

6. Two small metallic spheres, each of mass m = 0.200 g, are suspended as pendulums by light strings of length L. The spheres are given the same electric charge of 7.2 nC, and they come to equilibrium when each string is at an angle of = 5.00° with the vertical. How long are the strings?

7. A proton is placed in an electric field of intensity 800 N/C. What are the magnitude and direction of the acceleration of the proton due to this field? (e = 1.60 × 10-19 C, mproton = 1.67 × 10-27 kg)

8. A small styrofoam ball of mass 0.120 g is placed in an electric field of 6000 N/C pointing downward. What charge must be placed on the ball for it to remain suspended in the field?   

Please explain your work

Explanation / Answer

HI, i am answering questions 4,5,7,8 here

4) radius of shell, r= 14cm,

charge q=32mC = 32x 10^-3 C
a) electric field at 10cm =?
  inside the shell there is no charge, thus, electric field at 10cm = 0
b) at distance 20cm from center,
E= q/ (4**r^2) = 32*10^-3/ (4*3.14*8.853x10^-12* 0.2^2) = 7.19 x10^9 N/C

5)
F = (q x q) / (4 x x x r^2)

F = Electric Force
q = magnitude of the two charges
= Electric Constant (8.85 x 10^(-12) F/m)
r = distance between the 2 charges


by newtons law F = ma, .
F = (0.001) x (414) = 0.414N

by Coulomb's Law,
F = (q x q) / (4 x x x r^2)
0.414 = (q^2) / (4 x (3.14) x (8.85 x 10^(-12)) x (0.02)^2)

thus , q = 1.35674 x 10^(-7) C = 1.35 x 10^(-7) C

7) F= ma = qE = 1.60 × 10-19C x 800 N/C = 1.280x 10-16N
a = 1.28x10-16 / 1.67 × 10-27 = 7.66x10^10 m/s
the direction will be in the direction of the electric field.

8)
by formula qE=mg
q=0.120x10^-3x9.8/E=1.176x10^-3 /6000=0.196x10^-6 C
thus to remain suspended, the charge is to be -0.196x10^-6 C

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