Recent content by jj364

Hi, the notation used for defining vectors and parameters is just the one in the question and I didn't want to confuse the vector x with a cross product, so I used the other notation for cross product, nevertheless I accept that it was a bit confusing, apologies. Ok I see this totally, makes...

Homework Statement Four 3-vectors a, b, c, and d are related by the equation ax + by + cz = d; where x, y, and z are real parameters. Using a suitable combination of scalar and vector products, findd x, y, and z in terms of the vectors Homework Equations The Attempt at a...

Yes sorry, wasn't being very clear, I did mean the k component of n hat there yes. Ok I see the problem with the normalisation factor there, should be 4x2 and 4y2, thank you very much!

Homework Statement (i) Find the normal, n, at a general point on the surface S1 given by; x2+y2+z = 1 and z > 0. (ii) Use n to relate the size dS of the area element at a point on the surface S1 to its projection dxdy in the xy-plane. The Attempt at a Solution To...

Oh right I see, misread the question, didn't realize that it was charge not current. So you can write ΔB=QR/NA. Thanks very much!

Current is the rate of flow of charge. So could I say from this that B=IR/NA? Because I'll have a rate on either side of my equation?

Homework Statement A wire loop of area 2·0×10−4 m2 contains 40 turns, and has a total resistance of 40Ω. The plane of the loop is perpendicular to a uniform magnetic field of magnitude B0. The magnetic field is now turned off such that the flux through the loop drops linearly to zero. A total...

Actually I think I might have worked it out. I think it is just the solutions to z^3=1 so 1, e\frac{2\pi i}{3}, e\frac{4\pi i}{3} I tried it for the equations and it worked, is this right? They are all rotations of 2pi/3 of each other so it does make sense.

Ok, so does it rotate them by 2π/3 keeping the same magnitude? But I'm still struggling to work out my problem from this. Do I need to just think about it or can I actually solve the problem using the equations, because I've tried eliminating to no avail?

Ok I think I've worked it out now, I wrote out the differential equation and the auxiliary equation gave me answers of m=Aex + Bex(\frac{-1}{2}+\frac{\sqrt{3}}{2}) + Cex(\frac{-1}{2}+\frac{-\sqrt{3}}{2}) Which I can solve using initial conditions to get A=B=C=1/3 so the final sum is...

I'm still a little confused I think. I managed to get the the differential equation whose auxiliary equation is m^3-1=0 which is what I solved in the previous section but for complex numbers not real, or does it not matter? Because if I use my solutions for z^3-1=0 then I end up with very...

Ah thanks! Makes it a lot easier to read. Not so good at LaTeX!

Homework Statement Find the sum of the series \displaystyle S_1=1 + \frac{x^3}{3!}+\frac{x^6}{6!}+\,\dots Can't seem to get the bit above to show up nicely, should be 1+x^3/3! +x^6/6! +... Sorry! Homework Equations In a prior part of the question I had to find the complex roots of z3-1=0...

I'm sorry I don't know. I thought that the chain rule for partial derivatives was; \frac{du}{dz} = (\frac{\partial u}{\partial x})y(\frac{dx}{dz}) + (\frac{\partial u}{\partial y})x(\frac{dy}{dz})

Sorry mis read that!