Force on Moving Charges in a Magnetic Field

AI Thread Summary
The discussion focuses on determining the direction of the magnetic force on a positive charge moving in the xy plane within a magnetic field directed along the z-axis. The relevant equation is the cross product, which is essential for calculating the Lorentz force. Participants express confusion about applying the formula and evaluating the cross product of the velocity vector and the magnetic field vector. Clarification on how to plug in the values and interpret the equation is sought. Understanding the cross product is crucial for solving the problem accurately.
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Homework Statement


Consider the example of a positive charge q moving in the xy plane with velocity \hat{v} = vcos(\theta)\hat{x} + vsin(\theta)\hat{y} (i.e., with magnitude v at angle \theta with respect to the x-axis). If the local magnetic field is in the +z direction, what is the direction of the magnetic force acting on the particle?
Express the direction of the force in terms of \theta, as a linear combination of unit vectors, \hat{x}, \hat{y}, \hat{z}.


Homework Equations


Cross product.
\vec{C} = \vec{A} X \vec{B} = (AxBy - AyBx)\hat{z} + (AyBz - AzBy)\hat{x} + (AzBx - AxBz)\hat{y}


The Attempt at a Solution


I don't know what to plug in, and overall am just confused as to what the formula means.

Any explanation would be greatly appreciated!
 
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You only need to to apply the equation for the Lorentz force here. What have you learned about how to evaluate the cross product of two vectors?
 
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