\( coil of 1000 tums and cross-sectional area of \(5 \mathrm{~cm}^2\) is at right angle to a flux of \(2 \times 10^{-2} \mathrm{~T}\), which is reduced to zero in 10 seconds. Calculate the induced e.m.f.
A. \(1.0 \times 10^{-5} \mathrm{~V}\) B. \(5.0 \times\) \(10^{-3} \mathrm{~V}\) C. \(1.0 \times 10^{-3} \mathrm{~V}\) D. \(10.0 \times 10^{-5} \mathrm{~V}\)
Correct Answer: C
Explanation
No of turns \(\mathrm{N}=1000\)rea \(\mathrm{A}=5 \mathrm{~cm}^2=5 \times 10^{-4} \mathrm{~m}^2\) Magnetic flux \(\mathrm{B}=2 \times 10^{-2} \mathrm{~T}\) \(\Delta \mathrm{B}=2 \times 10^{-2}-0=2 \times 10^{-2} \mathrm{~T}\) time \(t=10 \mathrm{~S}\) required induced e. \(m \cdot f=\) ?orrelating equationsaraday's law of electromagnetic induction \(\mathrm{E}=-\mathrm{N} \frac{\Delta d}{\Delta t}\) with \(\phi=\mathrm{BA}\), \(\mathrm{E}=-\mathrm{NA} \frac{\Delta \mathrm{B}}{\Delta t}\) \(E=\frac{-100 \times 5 \times 10^{-4} \times 2 \times 10^{-2}}{10}\) \(\mathrm{E}=1.0 \times 10^{-3} \mathrm{~V}\) \(\mathrm{E}=1.0 \times 10^{-3} \mathrm{~V}\)