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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Physics (PH)
Electricity
first one is formula for electric field at point due to semi infinite wire on +ve z axis. second one is same for -ve z axis. my doubt is that if minus sign comes before second for why sign of r cap is not changing. if possible provide me derivation for second.
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Abhishek singh Best Answer
Here is the solution for positive line charge placed along positive Z direction. See the calculations carefully. physics behind this question is simple, but calculations are tricky, I have used substitution method for integration. As always, if you got stuck in any step, do it once again by yourself. Repeat the calculation from scratch if you got stuck anywhere. Gracious.
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It has been a long time, I haven't answered any questions on Eduncle. Today, I was scrolling some profiles and what I have seen is completely mind shattering. Both Tutors have mentioned same thing that r cap vector is always positive. If you are saying r cap a vector, there must exist -r cap. What is the physical meaning of r cap and -r cap? Let say in cylindrical coordinates, you are at r distance away from z axis. You can always have two direction at that point. One away from the z axis( r cap) and one towards the z axis(-r cap). You must have heard of centripetal and centrifugal forces. What is the difference between them( as per vector algebra). Centripetal is radially invards(-r cap) and centrifugal is radially outward (r cap).
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you are right... negative r cap is possible
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Chandra prakash
hope you get it dear.. 👍
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Chandra prakash
Why rcap is not negative? Infinite wire possess cylindrical symmetry and in cylindrical coordinate r is distance from z axis in all direction, or in other words there is no negative r direction in cylindrical and spherical coordinate system, therefore there is no negative direction in r but z can be positive or negative in cylindrical system. the negative direction concept is limited to Cartesian coordinate system only. Hope you got my point.
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I agree with sir.... it's best explanation of this prob.. best regards
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how could u say that, in spherical coordinate, r cap is direction outward from origin and negative r cap means direction towards the origin.. I am not getting this point that r cap is not negative. r cap is just showing direction... even u know centripetal force , it's direction is negative r cap means towards origin...
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please elaborate ur point.
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Ghost.
Did you remember when you write a vector in spherical or cylindrical system the , the components in radial direction is never been negative, because there is no negative direction, you don't need seperate derivation, if you can drive first formula then second one is same, just remember (-r cap) Direction doesn't exist, there is only r cap direction. Wishes
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Ghost.
Why rcap is not negative? Infinite wire possess cylindrical symmetry and in cylindrical coordinate r is distance from z axis in all direction, or in other words there is no negative r direction in cylindrical and spherical coordinate system, therefore there is no negative direction in r but z can be positive or negative in cylindrical system. the negative direction concept is limited to Cartesian coordinate system only. Hope you got my point.
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Abhishek singh![best-answer]()
Solution for the negative line charge placed along -Z direction. Calculations are exactly same as above part. Er and Ez calculations are exactly same(100% same). Where is the difference? just in vector directions! see the directions carefully. Think. Think. and Think. You are always free to ask doubts. Cheers!
yeah.. u r right..