Calculating Electric Fields of 3 Charges on a Line

[thekakaru]

Three charged objects are arranged on a vertical line as shown
in the figure. The separation between charges is 3.0 cm.

a) If you wanted to find the force on charge C, which
fields would be relevant? Explain and calculate the
magnitude of this field. Which direction does it point?

b) What is the force, magnitude and direction, acting on charge C?

 

[tiny-tim]

welcome to pf!

hi thekakaru! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[thekakaru]

I know in general how to find the Efields on charge C and the Eforces on charge C, but i was just confused if the Efield on C is either due to B or due to A and B.

 

[tiny-tim]

hi thekakaru!

everything affects everything else …

the force on C is the force from A plus the force from B ​

 

[rwisz]

a) In order to find the force on charge C, we would need to consider the electric fields created by charges A and B. This is because electric fields are vectors and can be added together to determine the total electric field at any given point. In this case, the electric field from charge A would point downwards towards charge C, while the electric field from charge B would point upwards towards charge C. The magnitude of each field can be calculated using the equation E = kq/r^2, where k is the Coulomb's constant, q is the charge, and r is the distance between the charges. In this case, the magnitude of the electric field from charge A would be E = (9x10^9 Nm^2/C^2)(5x10^-6 C)/(0.03 m)^2 = 0.111 N/C, and the magnitude of the electric field from charge B would be E = (9x10^9 Nm^2/C^2)(2x10^-6 C)/(0.03 m)^2 = 0.037 N/C.

b) The force acting on charge C would be the vector sum of the forces from charges A and B. Since the electric fields from charges A and B are in opposite directions, the force on charge C would be the difference between the two forces. This can be calculated using the equation F = qE, where q is the charge and E is the electric field. In this case, the force on charge C would be F = (5x10^-6 C)(0.111 N/C) - (2x10^-6 C)(0.037 N/C) = 0.444 N. The direction of this force would be downwards, towards charge A, since the electric field from charge A is stronger than the electric field from charge B.