field of a line charge

Hi

Could you please help me with this query? Thank you.

Regards
PG

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.

steveB said:

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.

Click to expand...

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

Thank you.

steveB said:

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.

Click to expand...

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

PG1995 said:

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

Click to expand...

Sorry, typo on my part and it should be z-direction.

I do get your point. To resolve the conflict in your example, imagine that we only care about |z|<0.0001 m. Now do the computation numerically and compare to the answer assuming the line in infinite in extent. You will see no significant difference in the answer. However, if |z|=2999m, there will be an error in assuming the extent is infinite. The scale is very important.

To give an similar example, imagine two equal charges Q separated by 1 cm. The field 10 cm away from these charges must be calculated using Coulombs law and superposition and using the exact positions of the charges. However, the field 1 km away can be approximated as a single charge of 2Q with position half way between the two charges. Again, the scale is important and you have to visualize it. Visualizing gets easier with experience.