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Induced emf and current due to a changin...

Induced emf and current due to a changing uniform B field
Figure 30-8 shows a conducting loop consisting of a half-circle of radius r = 0.20 m and three straight sections. The halfcircle lies in a uniform magnetic field `vecB` that is directed out of the page, the field magnitude is given by `B = 4.0t^(2) + 2.0t + 3.0`, with B in teslas and tin seconds. An ideal battery with emf `E_("bat")` = 2.0 V is connected to the loop. The resistance of the loop is 2.0 `Omega`.
(a) What are the magnitude and direction of the emf `E_("ind")` induced around the loop by field `vecB` at t = 10 s?
(b) What is the current in the loop at t = 10 s?

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To solve the problem step by step, we will break it down into two parts as specified in the question. ### Part (a): Finding the Induced EMF \( E_{\text{ind}} \) 1. **Identify the expression for the magnetic field**: The magnetic field is given by \( B(t) = 4.0t^2 + 2.0t + 3.0 \) (in teslas). 2. **Calculate the magnetic field at \( t = 10 \) seconds**: \[ ...
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