Find q1 such that Force on Test Charge has no X-Component

AI Thread Summary
To ensure the force on a test charge at (5,0,6) has no x-component, the electric field contributions from point charges q1 and q2 must balance in the x-direction. Given q2 is 4nC at (2,0,1), the position of q1 at (4,0,-3) can be adjusted by calculating the required value for q1. The test charge's nature does not affect the calculations, as any non-zero charge will suffice. The focus is on determining the correct magnitude and sign of q1 to achieve the desired force condition. The solution requires applying principles of electrostatics to find the appropriate value for q1.
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There are two point charges q1 located at (4,0,-3) and q2 at (2,0,1) if q2=4nC find q1 such that the force on a test charge at (5,0,6) has no x-component. I think I would know how to do this problem if I knew what a test charge was. Is it just one electron.
 
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The point is that doesn't matter what the charge is (as long as it's not zero). If you were to place a charge q_3 at (5, 0, 6) what would q_1 have to be in order that the force acting on q_3 due to the electric field produced by q_1 and q_2 would give zero x component.
 
thanks for your help
 
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