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Four non-conducting wires each with mass m = 1 kg and length ℓ = 2.0 m are joined to form a square. They have charge with charge per unit length 1 c/m and –1 c/m shown in figure. Initially the square is kept on x–y plane and there exists uniform electric field N E 4C  along Z-direction. If the square is released from rest: will it perform oscillatory motion ? will it perform shm? what will be it's maximum angular speed?
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Four non-conducting wires each with mass m = 1 kg and length ℓ = 2.0 m...


Analysis of the Square's Motion


Performing Oscillatory Motion:
- Yes, the square will perform oscillatory motion due to the electric forces acting on each wire.

Performing Simple Harmonic Motion (SHM):
- The square will perform SHM as the restoring force acting on each wire is proportional to the displacement from the equilibrium position.

Maximum Angular Speed:
- The maximum angular speed can be calculated using the equation for SHM: ω = sqrt(k/m), where k is the force constant and m is the mass of each wire.
- The force constant k can be calculated as the product of the charge per unit length and the electric field strength.
Explanation:


Oscillatory Motion:
- The electric forces acting on each wire will cause the square to rotate about its center, leading to oscillatory motion.

Simple Harmonic Motion (SHM):
- The restoring force acting on each wire is directly proportional to the displacement from the equilibrium position, leading to SHM.

Maximum Angular Speed Calculation:
- The force constant k is given by k = (charge per unit length) * E = 1 * 4 = 4 N/m.
- Substituting k = 4 N/m and m = 1 kg into ω = sqrt(k/m), we get ω = sqrt(4/1) = 2 rad/s.
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Four non-conducting wires each with mass m = 1 kg and length ℓ = 2.0 m are joined to form a square. They have charge with charge per unit length 1 c/m and –1 c/m shown in figure. Initially the square is kept on x–y plane and there exists uniform electric field N E 4C  along Z-direction. If the square is released from rest: will it perform oscillatory motion ? will it perform shm? what will be it's maximum angular speed?
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Four non-conducting wires each with mass m = 1 kg and length ℓ = 2.0 m are joined to form a square. They have charge with charge per unit length 1 c/m and –1 c/m shown in figure. Initially the square is kept on x–y plane and there exists uniform electric field N E 4C  along Z-direction. If the square is released from rest: will it perform oscillatory motion ? will it perform shm? what will be it's maximum angular speed? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Four non-conducting wires each with mass m = 1 kg and length ℓ = 2.0 m are joined to form a square. They have charge with charge per unit length 1 c/m and –1 c/m shown in figure. Initially the square is kept on x–y plane and there exists uniform electric field N E 4C  along Z-direction. If the square is released from rest: will it perform oscillatory motion ? will it perform shm? what will be it's maximum angular speed? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four non-conducting wires each with mass m = 1 kg and length ℓ = 2.0 m are joined to form a square. They have charge with charge per unit length 1 c/m and –1 c/m shown in figure. Initially the square is kept on x–y plane and there exists uniform electric field N E 4C  along Z-direction. If the square is released from rest: will it perform oscillatory motion ? will it perform shm? what will be it's maximum angular speed?.
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