Why Is Sin A Used in the Cross Product Equation F=qvBsinA?

In summary, sin A of a cross product is the sine of the angle between two vectors in a cross product and is calculated by multiplying the magnitudes of the vectors and the sine of the angle between them. It has a range of values between -1 and 1 and is commonly used in various scientific fields. It can be negative when the angle between the vectors is greater than 180 degrees.
  • #1
glueball8
346
1

Homework Statement



Just a general questions I don't understand. Why is it sin A in a cross product and not cos A?
I don't understand it in the equation F=qvBsinA

Homework Equations



no

The Attempt at a Solution



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  • #2
nvm.. got it...
 
  • #3


In a cross product, the sine of the angle between two vectors is used because it represents the magnitude of the perpendicular component of one vector onto the other. This is important in calculating the force (F) exerted on a charged particle (q) moving with velocity (v) in a magnetic field (B), as the perpendicular component of the velocity to the magnetic field is what causes the particle to experience a force. This is why the sine of the angle (A) is used in the equation F=qvBsinA. If the cosine of the angle was used, it would represent the magnitude of the parallel component of the velocity, which does not contribute to the force experienced by the particle. Therefore, the use of sine in the cross product allows for a more accurate calculation of the force.
 

Related to Why Is Sin A Used in the Cross Product Equation F=qvBsinA?

1. What is sin A of a cross product?

Sin A of a cross product refers to the sine of the angle between two vectors in a cross product. It is a mathematical calculation used to determine the magnitude of the resulting vector in a cross product.

2. How is sin A of a cross product calculated?

The calculation for sin A of a cross product is the product of the magnitudes of the two vectors and the sine of the angle between them. This can be represented by the formula: sin A = |A| * |B| * sin(theta), where |A| and |B| are the magnitudes of the vectors and theta is the angle between them.

3. What is the range of values for sin A of a cross product?

The range of values for sin A of a cross product is between -1 and 1, inclusive. This means that the resulting vector in a cross product can have a magnitude between the negative and positive magnitudes of the two vectors multiplied by the sine of the angle between them.

4. How is sin A of a cross product used in science?

Sin A of a cross product is used in various scientific fields, such as physics, engineering, and mathematics. It is especially useful in calculating the magnitude of force or torque in a system that involves multiple vectors and angles.

5. Can sin A of a cross product be negative?

Yes, sin A of a cross product can be negative. This occurs when the angle between the two vectors is greater than 180 degrees, resulting in a negative magnitude for the resulting vector in the cross product.

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