Recent content by steroidjunkie

Homework Statement Using free electron model find the number of electron quantum states per unit volume in ##[\varepsilon_F, \varepsilon_F + \Delta \varepsilon]## energy interval of sodium. Fermi energy of sodium is ##\varepsilon_F = 3.22 eV##, and energy band width is ##\Delta...

I have one more question. Does it matter what charge I put at ##x_1##? I just inserted ##Q_3## in the ##F_{13}+F_{23}=0## equation and it doesn't matter if ##Q_3## is positive or negative. I always get ##0=0##. That would mean ##Q_3## can be positive or negative. Or not?

I get it, but I switched the plus sign to minus in ##k \cdot \frac{Q_1 \cdot (-Q_3)}{x_1^2}=-k \cdot \frac{Q_1 \cdot (-Q_3)}{x_1^2}## Now I can divide equation by minus and I will get the same equation as was for positive ##Q_3##. Right?

I see I've made some typing errors and my notation for distance of ##Q_3## from charge ##Q_1## isn't appropriate. Also, when ##x_1=-3cm## charge ##Q_3## must be negative because it is closer to the positive charge. If it was positive, it'd be repelled. Thank you all for your help and pointing...

##F_{13}+F_{23}=0## or ##F_{13}=-F_{23}## If I follow through with this then: ##9 \cdot x_1^2+18 \cdot r x_1+9 \cdot r^2=-(-16) \cdot x_1## ##9 \cdot x_1^2+18 \cdot r x_1+9 \cdot r^2-16 \cdot x_1=0## ##-7 \cdot x_1^2+18 \cdot r x_1+9 \cdot r^2=0## ##-7 \cdot x_1^2+18 \cdot 7 x_1+9 \cdot 7^2=0##...

Homework Statement Two point charges ##Q_1 = 9 \mu##C and ##Q_2 = -16 \mu##C are fixed in space on a distance r=7cm. At what distane ##x_1## from the first charge, and ##x_2## from the second charge, should we place the third charge ##Q_3## so that net force on ##Q_3## is zero? make a sketch...

You're right. It's 2 minutes, and not 4 minutes. Thank you very much for helping me.

OK, than: ##\tan 45=\frac{m \cdot g}{q_1 \cdot E}## ##\tan \Theta_2=\frac{m \cdot g}{q_2 \cdot E}## ##q_1=q, q_2=q_1-40\%=q-0.4q=0.6q####\tan 45=\frac{m \cdot g}{q \cdot E}## ##\tan \Theta_2=\frac{m \cdot g}{0.6 \cdot q \cdot E}## ##q \cdot \tan 45=\frac{m \cdot g}{E}## ##0.6 q \cdot \tan...

Well, I could substitute ##\Theta_2##: ##mg=q \cdot E \cdot \tan(\Theta_2)## ##\tan(\Theta_{2})=\frac{mg}{q \cdot E}## ##\Theta_2=\arctan \frac{mg}{q \cdot E}## What do I do now? Do I just say that ##\Theta_2## is 60% of 45 degrees which is 27 degrees?

Homework Statement Charged metal sphere hanging on an isolated thread of negligible mass is put in a homogeneous horizontal electric field so that the thread makes a 45 degree angle with the el. field. What angle does the thread with the sphere close with the el. field after we remove 40% of...

I see. I could have stated that: ##pV^2=const## and then from the pressure equation: ## const=\frac{1}{a}ln(\frac{S}{\gamma})## Then I substitute variables in constant in order to get a dependence on T: ##pV^2=\frac{1}{a}ln(\frac{S}{\gamma}) \rightarrow apV^2=ln(\frac{S}{\gamma}) \rightarrow...

Regarding a mistake with (a) ##T=\frac{1}{aV} \cdot \frac{\gamma}{S} \cdot \frac{1}{\gamma}=\frac{1}{aSV}## Thank you for noticing. This leads to: ##C_V=(\frac{d}{dT})_V TSpaV^2=SpaV^2## (b) The right formula: ##C_V=(\frac{dH}{dT})_p## ##H=U+pV=U+U=2U## ##C_p=(\frac{d}{dT})_p (2U)=2 \cdot...

Homework Statement Find: (a) Equation of state $$f (p, V, T)$$ and (b) Adiabatic equation in dependence on volume and pressure. Internal energy $$U(V, S)=\frac{1}{aV} ln(\frac{S}{\gamma})$$ where a and ##\gamma## are positive constants. Homework Equations (a) ##dU=TdS-pdV \rightarrow##...

I think i found the solution. I need to show that f(G) is a nonempty set and that for every g1 and g2 element f(G): g1*g2-1 element f(G) by prooving four axioms of group. And the answer to the second question is: homomorphism of an identity is an identity and homomorphism of an inverse is an...

Thank you for your guidelines. This is what I came up with: (click on the picture to show it and again to see it clearly)