- #1
grantrudd
- 7
- 0
this is the second part of a 3 part question the first part was:
A uniform circular ring of charge Q=4.40 microCoulombs and radius R=1.30cm is located in the x-y plane, centered on the origin as shown in the figure. What is the magnitude of the electric field E at point P, located at z=3.30 cm?
i used E=F/q and integrated to get the formula
E=KQz/(z^2+a^2)^3/2 and got an answer of 2.92x10^7 N/C, which was right
now onto my question
Consider other locations along the positive z-axis. At what value of z does E have its maximum value?
i figure the equation i figured out in part 1 of this question would be relevant
E=KQz/(z^2+a^2)^3/2
i decided to take the derivative with respect to z of the equation above, and i believe that might be where i am making a mistake. to save the hassle of writing out the long work, here is what i got.
dE/dz= -1.5KQz(z^2+a^2)^1/2
the only critical point i am getting from this derivative is z=0, which makes sense because the electric field is at a minimum at that point. I am thinking that as z approaches infinity, the cosine between the individual vectors and the resultant vector approaches 1, which would lead to a maximum. can anyone tell where i went wrong or if my logic is off?
thanks
Grant
A uniform circular ring of charge Q=4.40 microCoulombs and radius R=1.30cm is located in the x-y plane, centered on the origin as shown in the figure. What is the magnitude of the electric field E at point P, located at z=3.30 cm?
i used E=F/q and integrated to get the formula
E=KQz/(z^2+a^2)^3/2 and got an answer of 2.92x10^7 N/C, which was right
now onto my question
Homework Statement
Consider other locations along the positive z-axis. At what value of z does E have its maximum value?
Homework Equations
i figure the equation i figured out in part 1 of this question would be relevant
E=KQz/(z^2+a^2)^3/2
The Attempt at a Solution
i decided to take the derivative with respect to z of the equation above, and i believe that might be where i am making a mistake. to save the hassle of writing out the long work, here is what i got.
dE/dz= -1.5KQz(z^2+a^2)^1/2
the only critical point i am getting from this derivative is z=0, which makes sense because the electric field is at a minimum at that point. I am thinking that as z approaches infinity, the cosine between the individual vectors and the resultant vector approaches 1, which would lead to a maximum. can anyone tell where i went wrong or if my logic is off?
thanks
Grant