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A Rowland ring of mean radius $15 \mathrm{~cm}$ has 3500 turns of wire wound on a ferromagnetic core of relative permeability 800 . What is the magnetic field $B$ in the core for a magnetising current of $1.2 \mathrm{~A}$ ?
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Verified Answer
Magnetic field $B$ in the core
$$
\begin{aligned}
B &=\mu_m n I=\frac{\mu_m N I}{2 \pi r} \\
B &=\frac{\mu_0 \mu_r N I}{2 \pi r}=\frac{4 \pi \times 10^{-7} \times 800 \times 3500 \times 1.2}{2 \pi\left(15 \times 10^{-2}\right)} \\
&=4.48 \mathrm{~T}
\end{aligned}
$$
$$
\begin{aligned}
B &=\mu_m n I=\frac{\mu_m N I}{2 \pi r} \\
B &=\frac{\mu_0 \mu_r N I}{2 \pi r}=\frac{4 \pi \times 10^{-7} \times 800 \times 3500 \times 1.2}{2 \pi\left(15 \times 10^{-2}\right)} \\
&=4.48 \mathrm{~T}
\end{aligned}
$$
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