JEE PYQ: Electromagnetic Induction Question 7
Question 7 - 2020 (03 Sep Shift 2)
A uniform magnetic field $B$ exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate $dB/dt = 0.032$ Ts$^{-1}$. The induced current in the loop is close to (Resistivity of the metal wire is $1.23 \times 10^{-8};\Omega$m):
(1) 0.43 A
(2) 0.61 A
(3) 0.34 A
(4) 0.53 A
Show Answer
Answer: (2)
Solution
Length of wire $l = 30$ cm, so side of square $= l/4$. Area $A = (l/4)^2$. EMF $= \frac{dB}{dt} \times A$. Resistance $R = \rho \frac{l}{\pi r^2}$. Current $i = \frac{|dB/dt| \times (l/4)^2}{\rho l / (\pi r^2)} = \frac{0.032 \times (\pi \times 2 \times 10^{-3})^2}{1.23 \times 10^{-8} \times 0.3} = 0.61$ A.
BETA
