Recent content by emmett92k

What I end up with is: ##E_+=\frac{Q}{2\pi\epsilon_0} \frac{1}{\sqrt{a^2+z^2}}## Is this the answer I should've gotten?

Quick question, those the upper limit stay as ##\phi##? Thanks for all the help with this question, hopefully it all pays off.

Sorry don't know how I did that: ##\hat{r}=sin{\theta}cos\phi\hat{x}+sin{\theta}sin\phi\hat{y}+cos\phi\hat{z}##

Yeah so: ##\hat{r}=cos{\theta}sin\phi\hat{x}+sin{\theta}cos\phi\hat{y}+cos\phi\hat{z}##

Did you see I left two comments there? Because my first comment is what is on that page? Do you mean ##\hat{r}=\frac{\vec{r}}{r}##

Actually is it: ##x=rcos{\theta}sin\phi## ##y=rsin{\theta}cos\phi## ##z=rcos\phi##

Spherical coordinates are ##(r,\phi,\theta)## and cartesian is ##(x,y,z)##. ##r=\sqrt{x^2+y^2+z^2}##, ##\theta=tan^{-1}\big(\frac{y}{x}\big)##, ##\phi=cos^{-1}\big(\frac{z}{r}\big)## How do I precede from here?

For ##E_+## is ##\hat{r}## r(0,a,z)?

So does that mean I split the circle into two semi-circles and use the same method as (a) but change \lambda = \frac{Q}{2{\pi}R} to \lambda = \frac{Q}{{\pi}R} because its half the circumference?

Sorry I've found the mistake, the 2 multiplies by a half and cancels. As regards part (d) do I treat it as a dipole and use the formula: E(r,\theta) = \frac{qd}{4{\pi}{\epsilon}r^3}(cos{\theta}\hat{r}+sin\dot{\theta}\hat{\theta})

Ok I'm starting to follow now. The r values will be the distance of the hypotenuse if I draw a triangle. So: r_1 = \sqrt{a^2 + z^2}, r_2 = \sqrt{b^2 + z^2} So I sub them and differentiate to get: E = \frac{Q}{4\pi\epsilon}\Bigg[\frac{2z}{(a^2+z^2)^\frac{3}{2}} -...

Well the first two terms would be equal to zero. How do I differentiate the ##z## part if there is no ##z## variable?

Ok thanks for all the help by the way. For part (c) I know its partial differentiation but what will I differentiate with respect to? Will I do r_1 and r_2 separately?

Ah so I end up with V_1 = \frac{Q}{4{\pi}r_1\epsilon}, V_2 = \frac{-Q}{4{\pi}r_2\epsilon} This give a total V of: V = \frac{Q}{4\pi\epsilon}\Bigg[\frac{1}{r_1} - \frac{1}{r_2}\Bigg] Is this correct?

Is the integral of ##dq## not the integral of Rd\theta?