Question

a solenoid has 2000 turns wound over a length of 0.3m. the area of its cross section is 1.2* 10^-3 m. around its central section a coil of 300 turns is wound. if an initial current of 2A is reversed in 0.25s the e.m.f induced in the coil is equal to?

Answer 1

$\textbf{\Large{Hey there!}}$

$\large{\textsf{\underline{\bf{Given Data:}}}}\\\Large{N_1 =2000}\\N_2 = 300\\A = 1.2 \times 10^{-3} \; m^2\\L = 0.3 \ m\\I = 0.2 A\\t = 0.25 \ s}$

$\Large{\textsf{\bf{We know,}}}$

$\huge{\boxed{\textsf{Mutual Inductance }= \dfrac{\mu_o N_1 N_2 A}{L}}} }$

$\\AND,$

$\huge\boxed{{\textsf{Induce emf = }M \cdotp\frac{dI}{dt}}}$

$\mathcal{E} = \huge{ \dfrac{\mu_o N_1 N_2 A}{L}\cdotp\dfrac{dI}{dt}}}}\\\\\mathcal{E} = \dfrac{4\pi \times 10^{-7}\times 2000\times 300\times(1.2 \times10^{-3} )}{0.3}\cdotp\dfrac{2-(-2)}{0.25}\\\\\mathcal{E} = 0.048 \ V\\\\\boxed{\mathcal{E} = 0.48 \ mV}$

$\huge{\textsf{\bf{Hope It Helps You!}}}$