Question
A long solenoid of radius $a$ with $n$ turns per unit length is carrying a time-dependent current $I(t)=I_{0} \sin (\omega t)$ where $I_{0}$ and $\omega$ are constants. The solenoid is surrounded by a wire of resistance $R$ that has two circular loops of radius $b$ with $b>a$ (see the following figure). Find the magnitude and direction of current induced in the outer loops at time $t=0$.
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Here, $\mu_{0}$ is the permeability of free space, $n$ is the number of turns per unit length, and $I$ is the current passing through the solenoid. Show more…
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A long solenoid of radius $a$ with $n$ turns per unit length is carrying a time-dependent current $I(t)=I_{0} \sin \omega t \quad$ where $\quad I_{0}$ and $\omega$ are constants. The solenoid is surrounded by a wire of resistance $R$ that has two circular loops of radius $b$ with $b>a$. Find the magnitude and direction of current induced in the outer loops at time $t=0$.
A long solenoid, of radius $a$, is driven by an alternating current, so that the field inside is sinusoidal: $\mathbf{B}(t)=B_{0} \cos (\omega t) \hat{\mathbf{z}} .$ A circular loop of wire, of radius $a / 2$ and resistance $R,$ is placed inside the solenoid, and coaxial with it. Find the current induced in the loop, as a function of time.
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