The magnetic flux passing through a metal ring varies with time t as: phi_(B)=3(at^3-bt^2)T-m^2 with a=2.00s^-3 and b=6.00s^-2. The resistance of the ring is 3.0Omega. Determine the maximum current induced in the ring during te interval from t=0 to t=2.0s.
Answers
induced current is 0 A
given, The magnetic flux passing through a metal ring varies with time t as Φ = 3(at³ - bt²) T/m²
where a = 2 s^-3 and b = 6 s^-2
we know, induced emf, ε = -dΦ/dt
= -d{3(at³ - bt²)}/dt
= -3(3at² - 2bt)
= -9at² + 6bt
putting a = 2 , b = 6 and t = 2
so, ε = -9 × 2 × (2)² + 6 × 6 × 2
= -9 × 8 + 72
= 0
using Ohm's law, i = ε/R
= 0/3Ω = 0 A
so induced current is 0 A
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induced current is 0 A
given, The magnetic flux passing through a metal ring varies with time t as Φ = 3(at³ - bt²) T/m²
where a = 2 s^-3 and b = 6 s^-2
we know, induced emf, ε = -dΦ/dt
= -d{3(at³ - bt²)}/dt
= -3(3at² - 2bt)
= -9at² + 6bt
putting a = 2 , b = 6 and t = 2
so, ε = -9 × 2 × (2)² + 6 × 6 × 2
= -9 × 8 + 72
= 0
using Ohm's law, i = ε/R
= 0/3Ω = 0 A
so induced current is 0 A