Questions tagged [vectors]
Geometric object with magnitude (length) and direction.
2,600
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Physical intuition for the Minkowski space? [closed]
As the title suggests, I am looking for physical intuition to better understand the Minkowski metric.
My original motivation is trying to understand the necessity for distinguishing between co-variant ...
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1
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How does this proof of Gauss’ law generalize from $1$ to $n$ charges?
I am having trouble seeing how the proof of Gauss’ law for one charge generalizes to hold for multiple charges in Griffiths’ introduction to electrodynamics.
Gauss’ law is proved for one charge (for ...
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Split Pauli Four-vector as quadratic terms of spinors
If I have the Pauli Four-vector $$x_{\mu}\sigma^{\mu} = \left(\begin{array}{cc}
t+z & x-i y \\
x+i y & t-z
\end{array}\right)$$ with $\sigma^0$ as Identity Matrix. Is there some way to write ...
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Can sum of two vectors be a unit vector? [migrated]
I stumbled upon a question which states the following -
If vector $A = 0.6\bf\hat{i} + N\bf\hat{j}$ is a unit vector, find the value of $N$.
On solving, the value for $N$ would be 0.8 . But my real ...
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2
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How to find the resultant speed component, and finding the angle in which the trajectory had hit the ground?
When having a trajectory traveling over a projectile, both the vertical and horizontal velocity components must be obtained in order to calculate the resultant velocity.
The question is: Why the ...
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1
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How to go from a vector operator to its components?
(I'm sorry if this question is a duplicate, I couldn't find anything that answered my question.)
I'm doing an exercise where I'm supposed to get the matrix elements for the vector operator $D$ (the ...
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3
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$z$-component of electric field due to a static square loop
I am having trouble finding the $z$-component of an electric field discussed in problem 2.4 of Griffith’s introduction to electrodynamics.
Suppose we have a square loop of side length $a$ carrying a ...
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Why do we need unit vectors in a differential bit of area?
I was reviewing the section on spherical coordinates in Griffith’s’ introduction to electrodynamics and I noticed that he includes unit vectors in the definition of an infinitesimal bit of area but ...
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Covariant and contravariant velocity [migrated]
I'm facing the following problem in tensor calculus:
I want to calculate the velocity of a mass particle in spherical coordinates.
So I'm using the following coordinate functions for spherical ...
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Can a vector tangent to a spacelike surface be null?
I'm studying the peeling-off behaviour of zero rest-mass fields, as described in Penrose's paper. In it, he talks about the boundary $\mathscr{I}$ of the conformal completion of an asymptotically ...
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Complete unit of vectors and their scalar counterparts [closed]
I'm aware that we use m/s as the SI unit for both speed and velocity. My question then is, we use units to define the magnitude of the vector (velocity), why not add units for the direction too?
For a ...
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How can we find the angle between areal vector and magnetic field?
For finding torque we need to find the angle between areal vector and magnetic field. But areal vector makes an angle 37° with the x axis and that means it makes 53° with magnetic field because that's ...
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Why is angular velocity vector perpendicular to the velocity vector and position vector in uniform circular motion?
I am unable to understand if the angular velocity vector is always perpendicular to both the velocity vector and position vector how does it influence anything at all and what is it's significance. ...
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Possible ambiguities of quantization
Quantization means to replace $p$ (the momentum) in the expressions of classical physical quantities with $-i\hbar\nabla$, so we get an operator belonging to each physical quantity. However, an ...
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Confusion with treatment of unit vectors in electrostatics
I am reading Griffiths’ Introduction to Electodynamics and there are two problems where the methodology for treating unit vectors in integrals seems inconsistent to me.
When we are trying to find the ...
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