Charge in a Magnetic Field question

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SUMMARY

The discussion focuses on determining the i and j components of force on a charge in a magnetic field, specifically for a positive charge q. The participant references a coordinate system that indicates the direction of unit vectors and emphasizes the relationship between the direction of the induced current and the force experienced by the charge. The analysis concludes that the direction of the induced current—either clockwise or counterclockwise—eliminates certain options for the i and j components based on the provided diagrams.

PREREQUISITES
  • Understanding of magnetic fields and forces on charges
  • Familiarity with unit vector notation (i, j components)
  • Knowledge of induced current in circular loops
  • Basic grasp of coordinate systems in physics
NEXT STEPS
  • Study the right-hand rule for magnetic forces on charges
  • Learn about induced current in different geometries
  • Explore the relationship between current direction and magnetic field orientation
  • Review examples of force calculations in magnetic fields using vector components
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Lonewolf393
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Homework Statement


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These are two similar questions, one from my previous exam and one from a sample test my teacher provided. I understand how to work the problem, but my question is how is the i or j component decided in each of these?

Homework Equations



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The Attempt at a Solution


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There is a coordinate system provided that gives the direction of the unit vectors. The direction of the force on charge q (assuming it is positive) is the same as the direction of the induced current at the position of the charge if the dotted circle were a circular metal loop. The induced current can either be clockwise or counterclockwise. This eliminates all the ## \hat{j}## options in the first picture and all the ##\hat{i}## options in the second picture. The sign depends on whether you have clockwise or counterclockwise current flow. Can you figure that out?
 

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