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A projectile of mass m is fired from the surface of the earth of radius R at an angle α from the vertical with initial speed equal to (1/[sqrt 2]) the escape velocity.How high does the projectile rise?What is its range on earth's surface?Neglect air resistance and earth's rotation.
I solved the...
Re: vector problem
Observe one thing-in case of magnetic field,you cannot in general put forward a scalar potential given by grad V.
Here it is given...
I have talked to 4-5 forums regarding this.None but you are still lingering with a problem that does not seem to be done in wrong method.
Ok,I...
OK,A and B are vector fields having curl equal to zero.
We are to show div of (A+B)=0
Possibly the question is wrong.Except from some specific example it is not correct.Hence,cannot be proved.
Actually,since I wanted someone to say with me that this is wrong, posted this over...
Re: vector problem
The Fundamental Theorem of (Integral) Calculus is of the form:
(Lower Lt a,Upper Lt. b) ∫(df/dx)dx=f(b)-f(a)
where df/dx is often written as F(x).
So,when you use a cyclic integral,it means you are tking both the lower and upper limit to be the same...
We are bound to use...
Basic silly conceptual mistake.
rotational vector field means curl V is non-zero.
It can also be understood by commonsense.Curl measures the amount of rotation of a vector field.So,irrotational means curl V=0 and rotational means curl is non-zero.
k was also scalar when you extracted (f/k)...
You are simply WRONG.V is a vector field and by question,the curl is non-zero.
Added after 16 minutes:
I mean if the question is correct,then you are wrong.But if the question is wrong then you are correct.
Added after 22 minutes:
It is not convincing.You have missed a term...(f/k) is...
I am to show that Ñ.(A+B)=0 if
ÑxAis not=0
ÑxBis not=0
I suppose this is not a valid question.You please check.If it is a correct one then tell me how to start with.
Added after 7 minutes:
OK,that was a notation problem.
What we are given is that curl A or curl B are not equal to zero.
A vector field V is not irrotational.Show that it is always possible to find f such that fV is irrotational.
curl [fV]=f curlV-Vxgrad f
I have to equate the LHS to zero.But then,how can I extract f out of the resulting equation?
Please help
What is the wrong in the proof that there is no magnetic field?
We know:
div B=0 and B=curl A where B is the magnetic field and A is its vector potential
Then,∫div B dV=0=∫B.n dA(divergence theorem)
Thus, 0=∫(curl A).n dA
=∫A.dr(Stokes' theorem)
The last will be a cyclic integral.
Since...
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