The flux through a loop varies as Φ = at³ - bt² + ct, where a, b and c are positive constants. The induced current becomes zero at two positive instants whose sum is T. Find T.
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Question

The flux through a loop varies as Φ = at³ − bt² + ct, where a, b and c are positive constants. The induced current becomes zero at two positive instants whose sum is T. Find T.

G1 Physics · Accepted Answer

Current is zero when dΦ/dt = 3at² − 2bt + c = 0. The sum of roots is 2b/(3a), so T = 2b/(3a).