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If I'm understanding your question correctly, I think you have the concept correct and if the line of charge had finite length, you would be correct. However, this problem is essentially assuming an infinitely long line of charge in the x-direction. Hence, the location along the z-axis does not affect the cancellation (symmetry) that they are trying to take advantage of to make the problem easier.
If I'm understanding your question correctly, I think you have the concept correct and if the line of charge had finite length, you would be correct. However, this problem is essentially assuming an infinitely long line of charge in the x-direction. Hence, the location along the z-axis does not affect the cancellation (symmetry) that they are trying to take advantage of to make the problem easier.
Thank you.
Is that "x-direction" an intentional error, or, am I missing something here because they have line of charge along z-axis? I thought I should just confirm it. Thanks.
This is where concept of infinity messes up. Suppose, for the sake of argument, that we take infinity to be 3000m and the line of charge extends from -3000m to +3000m. Further suppose that the point P lies 5 units or meters above the positive y-axis. For the complete cancellation line of charge along the positive z-axis should extend to +3005m rather than +3000m. I hope you get my point. Thanks.
Regards
PG