Question

A rectangular loop of dimensions \(\ell=0.1\text{m}\) and \(w=0.05\text{m}\) moves with a constant velocity \(v=3\text{m/s}\) away from a long wire that carries a current \(I=10\text{A}\) in the plane of the loop (see figure). The total resistance of the loop is \(R=0.002\text{ Ohms}\). Find the magnitude of the current in the loop the instant the near side is a distance \(r=0.02\text{m}\) from the wire. For this problem, the velocity given is how \(r\) changes with time as the loop moves to the right. HINT: Find the flux in terms of \(r\), take the derivative with respect to time to find the induced emf. Use \(d/dt[\ln(u)] = (1/u)(du/dr)(dr/dt)\), with \(dr/dt\) as the \(v\) given.

Uploaded: 2023-09-18T17:44:52-08:00
Duration: 2 min 50 s
Channel: Supreeta N

          A rectangular loop of dimensions \(\ell=0.1\text{m}\) and \(w=0.05\text{m}\) moves with a constant velocity \(v=3\text{m/s}\) away from a long wire that carries a current \(I=10\text{A}\) in the plane of the loop (see figure). The total resistance of the loop is \(R=0.002\text{ Ohms}\). Find the magnitude of the current in the loop the instant the near side is a distance \(r=0.02\text{m}\) from the wire. For this problem, the velocity given is how \(r\) changes with time as the loop moves to the right. HINT: Find the flux in terms of \(r\), take the derivative with respect to time to find the induced emf. Use \(d/dt[\ln(u)] = (1/u)(du/dr)(dr/dt)\), with \(dr/dt\) as the \(v\) given.

A rectangular loop of dimensions ℓ=0.1m and w=0.05m moves with a constant velocity v=3m/s away from a long wire that carries a current I=10A in the plane of the loop (see figure). The total resistance of the loop is R=0.002 Ohms. Find the magnitude of the current in the loop the instant the near side is a distance r=0.02m from the wire. For this problem, the velocity given is how r changes with time as the loop moves to the right. HINT: Find the flux in terms of r, take the derivative with respect to time to find the induced emf. Use d/dt[ln(u)] = (1/u)(du/dr)(dr/dt), with dr/dt as the v given.

Added by Esperanza G.

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