Question 333: Electromagnetic Induction

Question

Let us consider two solenoids $$A$$ and $$B$$, made from same magnetic material of relative permeability $$\mu_r$$ and equal area of cross-section. Length of $$A$$ is twice that of $$B$$ and the number of turns per unit length in $$A$$ is half that of $$B$$. The ratio of self inductances of the two solenoids, $$L_A: L_B$$ is

Accepted Answer

$$\begin{aligned}
& L=\mu_0 \mu_r 	imes n 	imes A 	imes N \
& L=\mu_0 \mu_r n 	imes A 	imes \frac{N}{I} 	imes I \
& L=\mu_0 \mu_r 	imes n^2 	imes A 	imes I \Rightarrow L \propto n^2 I \
& \Rightarrow \frac{L_A}{L_B}=\frac{n_A^2}{n_B^2} 	imes \frac{I_A}{I_B} \
& \Rightarrow \frac{L_A}{L_B}=\frac{1}{4} 	imes 2=\frac{1}{2}
\end{aligned}$$

Answer

$$1: 2$$

Answer

$$2: 1$$

Answer

$$8: 1$$

Answer

$$1: 8$$

Electromagnetic Induction

Let us consider two solenoids $A and B, made from same magnetic material of relative permeability \mu_r and equal area of cross-section. Length of A is twice that of B and the number of turns per unit length in A is half that of B. The ratio of self inductances of the two solenoids, L_A: L_B$ is

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