Concept Combination
A ring lies on x-y plane such that a varying magnetic field B=kt is perpendicular to its plane.A current "I=10A" flows (clockwise) initially on the ring. Now a wave with small amplitude is generated on it.Find the fundamental frequency at t=2 k=2
Radius=2
Resistance of ring=π
Mass/length=1/π²
The answer is 1.
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1 solution
B=kt
Magnetic flux=ktπR²
|Emf|=kπR²
Current induced=kπR²/resistance=8
Induced current is anticlockwise
Net current=10-8=2 clockwise
Calculating the Tension force Taking elemental mass and equating tension and magnetic force on it
T(∆Q)=B×(net current)×R(∆Q)
T=B(2)R=8t
at t=2....T=16
For small amplitude wave v=√[T/(mass/length)] so v=√16π²=4π
Now,the wave must have ∆x=n(wavelength) to be a standing wave whose frequency will vary with time l.
=>2πR=1(wavelength)
[FUNDAMENTAL FREQUENCY] this gives frequency=4π/4π=1