What Distance from Charge \( q_1 \) Results in Zero Electric Field?

AI Thread Summary
To determine the distance from charge \( q_1 \) where the electric field is zero, the electric fields from both charges must be equal. The equation \( E_1 = E_2 \) leads to the relationship \( K(q_1/x^2) = K(q_2/(s-x)^2) \). By solving this equation, the distance \( x \) from \( q_1 \) can be expressed as \( x = s/(1 + \sqrt{q_2/q_1}) \). This formula indicates that the distance depends on the ratio of the charges and the total separation distance \( s \). The discussion emphasizes the importance of correctly defining variables to simplify the problem.
craigl34
Messages
3
Reaction score
0

Homework Statement



Two particles with positive charges q_1 and q_2 are separated by a distance s.

Along the line connecting the two charges, at what distance from the charge q_1 is the total electric field from the two charges zero?

(Express your answer in terms of some or all of the variables s, q_1, q_2 and K =1/(4*pi*\epsilon. If your answer is difficult to enter, consider simplifying it, as it can be made relatively simple with some work.)

Homework Equations



E = K*(q/(d)^2)
E_net = E1 + E2

The Attempt at a Solution



Since both the charges are positive, my E_net = E1 - E2. So I can solve this by finding where E1 and E2 are equal.

Setting the two equations equal I get K(q_1/s^2) = K(q_2/s^2)

Since I'm just concerned with finding the distance from q_1 to the point where the e-field is zero, wouldn't my equation be:

s_1 = (q_1 - (q_2/(s_2)^2)

Since none of the variables are defined, I'm having a hard time figuring out how to choose my 's' (distance). Wouldn't the distance ('s') depend on the magnitude of the charge on q_1 and q_2? How can I show that algebraically without somehow renaming the distance variable something other than 's'?
 
Last edited:
Physics news on Phys.org
I'm not sure I understood you.
s is a given distance between the two charges.
You need to find a point between them in which the field is zero - in other words, like you wrote, that E1 = E2.
Let's assume this point has the distance "x" from q1.
What is then the distance of this point from q2? (draw it to yourself if you're having a hard time).

Then use the appropriate formulas to deduce what x should be - in a similar manner to what you've done, but right this time :-)
 
See I understand that the distance from q_2 would be equal to (total separation 's' - distance from q_2), I just don't know how to represent that with only being able to use the variable 's' representing the total separation.
 
Nevermind, I figured it out.

I didn't realize that if I put in another variable into the equation 'x = distance from q_1' that it would end up cancelling out during the simplification process.

The answer for me would be:

x = s/1 + sqrt(q_2/q_1)
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'Calculation of Tensile Forces in Piston-Type Water-Lifting Devices at Elevated Locations'
Figure 1 Overall Structure Diagram Figure 2: Top view of the piston when it is cylindrical A circular opening is created at a height of 5 meters above the water surface. Inside this opening is a sleeve-type piston with a cross-sectional area of 1 square meter. The piston is pulled to the right at a constant speed. The pulling force is(Figure 2): F = ρshg = 1000 × 1 × 5 × 10 = 50,000 N. Figure 3: Modifying the structure to incorporate a fixed internal piston When I modify the piston...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top