1
vote
2answers
41 views

How do I find the perpendicular velocity of a particle to a varying magnetic field?

I am trying to find the component of velocity perpendicular to a magnetic field. This was easy when the magnetic field was static and pointing in only one direction (the $z$ axis), but now I need to ...
3
votes
2answers
560 views

Which mathematical operation does the right hand rule for current come from?

I am currently wondering about this famous rule: Where does it come from mathematically that when you point with your thumb in the direction of the current, your curved fingers will point in the ...
1
vote
1answer
60 views

Curl of a vector field with two different systems of coordinates

Let $$\mathbf{H} = H_x \mathbf{u}_x + H_y \mathbf{u}_y + H_z \mathbf{u}_z$$ be a vector field whose components are defined with respect to the unit vectors $\mathbf{u}_x$, $\mathbf{u}_y$ and ...
1
vote
3answers
154 views

More about the Right Hand Rule?

We started learning about electromagnetism in physics class, and the Right Hand Rule comes in handy as seems easy to use, but I'm curious as to how it actually works. I guess it's more of a math ...
4
votes
4answers
3k views

Why is current a scalar quantity?

Current has both magnitude and direction. As per the definition of vector defined in encyclopedia, current should be a vector quantity. But, we know that current is a scalar quantity. What is the ...
2
votes
1answer
82 views

$\hat{\imath}$ component of force exerted on an electron by a magnetic field?

The magnetic field over a certain range is given by $\vec{B} = B_x\hat{\imath} + B_y\hat{\jmath}$, where $B_x= 4\: \mathrm{T}$ and $B_y= 2\: \mathrm{T}$. An electron moves into the field with a ...
0
votes
2answers
785 views

Electromagnetic wave propagation through two lossless dielectrics

In Elements of Electromagnetics (Sadiku, 3rd edition, Section 10.8), the author says to consider two lossless dielectric materials joined at an interface $z=0$. Here two lossless dielectric materials ...
1
vote
1answer
368 views

Induced voltage of a conductor in a magnetic field

A book which I referenced for Electrical Machinery states that the voltage induced in a conductor inside a magnetic field is given by $$ \mathcal{E}=(\mathbf{v} \times \mathbf{B})\cdot \mathbf{l}$$ ...
4
votes
2answers
155 views

Vector potential

I have difficulty understanding the following vector calculus example. Text can be found here. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a ...
0
votes
2answers
422 views

Why or how is cross product used?

I do not understand how does the result of two vectors acting on a particle require me to take the cross product to find the resultant. Won't the actual force on the particle be the result of the ...
1
vote
3answers
98 views

Currents and magnets

I've watched this video on YouTube by Sixty Symbols entitled "Currents and Magnets". In the video, the professor demonstrates the expansion of a wire due to current heating it up and he also ...
2
votes
1answer
1k views

Which are other anomalies like Divergence of 1/r^2?

As one might have learned in the basic science (ex. Electrodynamic theory), when we apply the divergence theorem to the vector function like 1/r^2 with it pointing in the radial direction (like ...
1
vote
2answers
475 views

Potential of surface charge

I have a question about the $ \hat{n} $ in this formula $\sigma = P \dot{}\hat{n}$. Why do sometime in my book they get $\sigma = P \cos{\theta}$ for a sphere. Isn't $\hat{n} = r$ ? And then in ...
1
vote
1answer
244 views

Is there a more clever way to apply the cross product of two vectors to magnetism?

I am just beginning to learn magnetism and my book used two ways to define the force caused by the magnetic field, brushing over the latter. The first: $$F = q v B \sin (\theta).$$ And: ...
0
votes
3answers
1k views

Direction of Magnetic force from a current running through a coil of wire

What is the direction is the magnetic force vectors pointing from a coil of wire that has current running through it? ...