Calculate R from Electric field lines.

[physics16102]

1. The problem statement
The electric field E (arrows) is produced by a point charge. Find R in meters

Homework Equations

E(due to pt charge) = kq/R^2
# of field lines/unit area represents relative field strength (only statement in my notes that seems to apply to problem)

The Attempt at a Solution

I assumed the two areas are equal, and the relative strengths are 5Q and 2Q, respectively. Then, k5Q/(1.5)^2 = k2Q/R^2 I solved and got .77, and neither .77 or 1.5+.77 are answer choices so I am obviously wrong. This problem is obviously supposed to be very easy since it is the first one on my practice test but it is nothing like anything in the book or examples done is class so I am clueless.

 

[physics16102]

If anyone knows where to start on this problem or can point me in the right direction, it would be greatly appreciated. I have access to online tutoring through cengage and two tutors were unable to help me with it so I am getting desperate.

 

[ehild]

Q is the same for both distances. It is the electric field, E=kQ/r^2 which is E=5 for r=1.5 and E=2 for r=R.

ehild

 

[physics16102]

Thank you! My notes have Q varying with the amount of electric field lines, which is where I was mistaken. The problem makes sense now

 

[rwisz]

I would first clarify the problem statement. Are we trying to find the distance R from the point charge to the areas where the electric field strength is 5Q and 2Q, respectively? Or are we trying to find the magnitude of the electric field at those points?

Assuming we are trying to find the distance R, we can use the formula E = kq/R^2, where E is the electric field strength, k is the Coulomb's constant, q is the charge of the point charge, and R is the distance from the point charge.

To find R, we can rearrange the formula to R = √(kq/E). Plugging in the values given, with k = 9x10^9 Nm^2/C^2 and q = 1C, we get R = √(9x10^9 x 1 / 5) = 6x10^8 meters. This is the distance R from the point charge to the area where the electric field strength is 5Q. Similarly, for the area where the electric field strength is 2Q, R = √(9x10^9 x 1 / 2) = 9x10^8 meters.

It is important to note that the number of field lines does not directly represent the electric field strength. The relative field strength is inversely proportional to the distance squared, as shown in the formula. Therefore, the number of field lines can only provide a general indication of the relative strength of the electric field.