Exploring electromagnetism! 2!
A thin ring wire of radius a and resistance r is placed coaxially inside a long solenoid of length l and cross-sectional radius b . at t = 0 the solenoid is connected to a battery of emf V . If total circuit resistance is R find the maximum magnetic radial force per unit length acting on the ring wire.
All given values are in SI Units
Assume that current in the ring is the Induced current in accordance to Lenz's law and faraday's law only . no current flowing through the solenoid enters the ring
The solenoid can be taken as an ideal inductor in this case
Neglect the after effects of Induced electric field due to time-varying magnetic fields in this case
The solenoid is infinitely long and magnetic field can be taken as constant throughout the axis of solenoid
Take a = 1 0 , b = 2 0 , V = 1 0 , R = 1 0 , r = 1 0 , l = 1 0 .
Multiply your answer by 1 0 9 .
Neglect Mutual Inductance between ring and inductor
Round off answer to 3 decimals.
The answer is 7.854.
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2 solutions
Actually, shouldn't the question state " Neglect the effect of mutual induction on solenoid " rather than " Neglect mutual inductance between ring and solenoid" . After all, it is mutual induction that is causing current to be induced in the ring and hence a radial force .
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Yeah! That's right .
@Prakhar Bindal , edit the question bro...
GREAT JOB MR. PRAKHAR BINDAL.... LIKE MOST OF UR PROBLEMS AND THIS ONE TOO.. ABSOLUTELY BRILLIANT AND STUNNING PROBLEM..... JUST CAN'T STOP THINKING ABOUT IT... NICE PROBLEM BUDDY.... BY THE WAY HOW MUCH DID U GET IN Ai2TS 2?
I Got 152/201 . Not happy . Could have easily got 175-177 .
(36,60,56) CMP
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One suggestion bro! : Mention in the question to Neglect the mutual induction affect of ring on solenoid . ( As I got this answer on neglecting it )
What not happy???I remember scoring 152 in Aiits-2 to get air 5.Toppers was around 172.
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The papers level is never same every time and the competition too . My score was around 167 to get air - 5. Topper score was around 178...
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@Aniket Sanghi – Ya may be paper was different.Same ranks!!!great.Ours physics was good(61/67)Maths(48/67)Chem(43/67)
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@Spandan Senapati – In our one i guess maths was easy as i can see my score as P 56/67 , C 48/67 , M 63/67 ( yeah i recall , my score was to be 67 in maths but i did a marking error which i came to know after result , which dropped my rank from 4 to 5)
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@Aniket Sanghi – You are talking abt class 12 th aiits.I am telling 11th one.
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@Spandan Senapati – Are yeah 😂 I forgot about your class ....
@Spandan Senapati – Prakhar comment is of 12th aiits only I guess ... so I just forgot about yr class....:P
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@Aniket Sanghi – BRO its PRAKHAR! I Seriously hate people calling me Parkhar :P :P
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@Prakhar Bindal – I can understand Bro . But I guess this auto-correction of my tab can't :P
@Spandan Senapati – And yeah , keep it up...
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@Aniket Sanghi – Thanks...Yours rank is grt as well.......☺☺
Yeah i wasn't happy at all because i came out of the examination hall In around 2 hours (paper was scheduled from 4:30 to 7:30 and i came out at 6:30 . I Dont know but i did it in a great hurry and hence made a lot of silly errors. a score of 180 was definitely achievable in that exam coz 67 in each physics and maths was very easy to score if i would have checked my answers once again in that one hour
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@Prakhar Bindal – And sorry but don't you think your friend making things a more public.Like ranks in a solution??? and that too in Caps......
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@Spandan Senapati – Well he is silly i must say :P
What's yr score in AIITS 2 and What's yr centre ? @Anubhav Tyagi
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Find the value of i in solenoid by solving circuit
The ans comes out to be i = ( V / R ) ( 1 − e − R t / L )
Then find di/dt
Then use (or derive) M = μ ° η π a 2 and L = μ ° η π b 2 l
Current in ring i 2 = ( M / r ) d i / d t
Then magnetic force per unit length comes out to be
F = 1 0 π e − t R / L ( 1 − e − t R / L ) ( Better way to differentiate , take e − t R / L = x )
Differentiate and get the ans F = 2 . 5 π = 7 . 8 5 4 N