In the second part, I am afraid your application of energy conservation is not accurate; since in both points A and B you should be getting:
Kinetic energy = 0, Potential energy = ##\frac{1}{2} k A^2## for each of them, which do not give the expression required.
So, my approach would be to...
Thanks. But I am afraid I still can't see how the numerator is negative; that is:
$$y^x-1-xy^x+xy^{x-1}<0$$.
I was stuck with this expression before you pointed out. I think this part is the difficult one.
Prove that
$$ \frac{y^x-1}{xy^{x-1}(y-1)}<1$$
where x,y \in ℝ, x>1 and y>1.
I was able to prove it using calculus, but am wondering if there was another way of doing so, like exploiting some inequality-theorems which involves real numbers. I'll be glad if anyone can show me a way and...
Hi Jano,
I will be glad if you could elaborate on why the integral can't be a negative infinity.
Also, going by the definition you provided for L, doesn't the integral term on the left only indicate the total magnetic energy of all space only if it contains linear media so that $$\mathbf H...
Thanks ! The argument is quite illuminating. But it still bears some risks for it might run into troubles for topologically complicated loops which orient in a bizarre manner. Am looking for a rigorous approach.
Exploiting quasistatic approximation, if one wishes to calculate self-inductance of any loop, he is led to the following double line integral:
\oint\oint\frac{d\vec{l_{1}}\cdot d\vec{l_{2}}}{r},
where r is the distance between the length elements \vec{dl_{1}} and \vec{dl_{2}}.
Is this...
We know that many books have deduced Lorentz transformations through rigorous maths and they add little to our visions about what's going on. But in the pdf I have attached, I have tried to deduce this transformation with logical arguments. It is really simple and no tensors have been included...
Yeah right,
Many books (Halliday, for example) use Kirchhoff's loop law under changing magnetic fields and they use $\E_{L}$ in the equation. Actually, this very emf is the right hand side of the Maxwell's equation and they toggle it to the left hand side and denote it beside the solenoid in the...
Please see the attachment. There I have derived Kirchhoff's Voltage law from Faraday's Induction law. Reply me if I have done something wrong and also notify me if this proof has been made somewhere else.
Thanking you,
EMROZ