Final answer:
To calculate the electric field in a wire loop subjected to the time-varying magnetic field, Faraday's law of electromagnetic induction should be used. This requires integrating the magnetic field over the loop's area to find the change in magnetic flux and differentiating this with respect to time to find the emf. The electric field is then the emf divided by the length of the loop.
Step-by-step explanation:
Given that a magnetic field of a cylinder is expressed by B=[(5mT)rho]sin[(2 mot)t], we want to calculate the electric field inside a wire loop of radius p=0.02m, when t=3.5s. To calculate this, we would apply Faraday's law of electromagnetic induction, which states that the electromotive force in a closed circuit is equal to the rate of change of magnetic flux through the circuit. In this case, our magnetic field is changing over time, giving rise to an induced emf and thus an electric field.
The equation for the electromotive force (emf) is given by ε = -dφ/dt. The change in magnetic flux (φ) can be calculated by integrating the given magnetic field B over the area of the loop. This is followed by differentiating the flux with respect to time. The electric field (E) induced in the wire loop is then given by E = ε/(2πR), where R is the radius of the loop.
Based on the available information and assumptions, only an approximation of the result can be made, without being able to compute the precise value of the electric field strength due to the nature of the magnetic field equation. Additional information or simplifications would be needed to fully resolve the equation.
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