1. Four charges are of values and at positions as shown in the figure below. In this problem we will be considering the force that three of the charge exert on the fourth.

 

a. Find the x and y components of the total electric field at the location of the -1 µC charge due to the other three charges. 

b. Find the x and y components of the total electric force on -1 µC charge due to the other three charges. 

c. Find the magnitude and direction of the electric force on the -1 µC charge due to the other three charges.

 

 

2. A conducting sphere of radius 10cm has a spherical cavity inside it of radius 1 cm and centered at the center of the sphere. A total charge of 10 µC is placed on the sphere. 

a. What is the electric field at the surface of the sphere? 

b. What is the charge density on the surface of the sphere? c. A charge of -5 µC in placed at the center of the cavity. Find the total charge density on the inner and outer surfaces of the sphere.

 

 

3. Three charges of magnitude 1µC, -4 µC, and 3µC are fixed in place in the positions shown in the figure below. 

a. What is the electrical potential at the point (x=0, y= -2m). 

b. How much work do the other charges do on a 5µC charge if it is brought to (x=0, y= -2m) from infinitely far away? 

c. Find a value and location of a fourth charge which could be used to set the electrical potential at (x=0, y= -2m) equal to 0.

1 C 2m 3m 3 1m -1 2m 4u 2m