Cross product Question

In summary, the conversation is about finding the cross product of the time derivative of the electric field and the magnetic field. The speaker suggests using the product rule and the determinant form of the cross product to solve the problem. They also mention that the coordinate system is likely cartesian.
  • #1
gjfelix2006
11
0
Hi, my question is the following:

[itex]
\frac{\delta\vec E}{\delta t}\times \vec B = ?
[/itex]
In other words, how can i develop this cross product.
Are there any identity that reduces this product?
Thanks.
 
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  • #2
Do you have E as a function of time? What coordinate system are you taking the cross product in?
 
  • #3
of course E is a function of time, and i think for simplicity the coordinate system is cartesian. Thanks
 
  • #4
There is the product rule d/dt(E x B) = dE/dt x B + E x dB/dt. That's about all I can tell you unless you give us what E and B are explicitly (which is what I think berkeman was asking).
 
  • #5
gjfelix2006 said:
of course E is a function of time, and i think for simplicity the coordinate system is cartesian. Thanks
Fair enough. Take the derivative and use the determinant form of the cross product. That should get you what you need.

http://en.wikipedia.org/wiki/Cross_product
 

What is a cross product?

A cross product, also known as a vector product, is a mathematical operation that combines two vectors to create a new vector that is perpendicular to the original vectors. It is denoted by the symbol "x" and is commonly used in physics and engineering to calculate forces and moments.

How is a cross product calculated?

To calculate the cross product of two vectors, you must first determine the magnitude and direction of the resulting vector. This can be done using the formula:

|a x b| = |a| * |b| * sin(theta)
where a and b are the two vectors and theta is the angle between them. Once you have the magnitude, you can use the right-hand rule to determine the direction of the resulting vector.

What is the difference between a cross product and a dot product?

A dot product, also known as a scalar product, is a mathematical operation that results in a scalar (a single number) rather than a vector. It is calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them. The dot product is used to calculate work and energy, while the cross product is used to calculate torque and angular momentum.

What are some real-world applications of cross products?

Cross products have many real-world applications, including calculating the torque on a spinning object, determining the direction of a magnetic field, and calculating the magnitude of a force on a moving charged particle. They are also used in computer graphics to create 3D images and in navigation to determine the orientation of an object.

What are some common misconceptions about cross products?

One common misconception about cross products is that they are commutative, meaning that the order of the vectors does not matter. However, cross products are not commutative, and changing the order of the vectors will result in a different magnitude and direction for the resulting vector. Another misconception is that the cross product always results in a vector perpendicular to the original vectors, but this is only true when the vectors are at a 90-degree angle to each other.

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