This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Welcome back — been a while! Let's pick up where you left off. Here's the solution for Question 3: a) Induced emf Step 1: Identify given values and convert units. Number of loops, N = 150 Initial length, l_1 = 5 cm = 0.05 m Initial width, w_1 = 8 cm = 0.08 m Final length, l_2 = 7 cm = 0.07 m Final width, w_2 = 11 cm = 0.11 m Time interval, t = 0.15 s Magnetic field strength, B = 25 T Angle relative to the plane of the coil = 30^. Step 2: Calculate initial and final areas, and the change in area. Initial area: A_1 = l_1 × w_1 = 0.05 m × 0.08 m = 0.004 m^2 Final area: A_2 = l_2 × w_2 = 0.07 m × 0.11 m = 0.0077 m^2 Change in area: A = A_2 - A_1 = 0.0077 m^2 - 0.004 m^2 = 0.0037 m^2 Step 3: Determine the angle for magnetic flux calculation. The angle in the magnetic flux formula _B = B A is the angle between the magnetic field vector and the normal to the coil's plane. Since the magnetic field is 30^ relative to the plane of the coil, the angle with the normal is: = 90^ - 30^ = 60^ Step 4: Calculate the change in magnetic flux. The change in magnetic flux is due to the change in area: _B = B A _B = 25 T × 0.0037 m^2 × (60^) _B = 25 × 0.0037 × 0.5 = 0.04625 Wb Step 5: Calculate the induced emf using Faraday's Law. Faraday's Law of Induction states: E = -N ( _B)/( t) E = -150 × 0.04625 Wb0.15 s E = -150 × 0.308333... V E = -46.25 V The magnitude of the induced emf is: a) E = 46.25 V b) Energy dissipated in the circuit Step 6: Calculate the power dissipated. Given the total internal resistance, R = 100 ohms. The power dissipated in the circuit is given by: P = E^2R P = (46.25 V)^2100 ohms P = 2139.0625 V^2100 ohms = 21.390625 W Step 7: Calculate the total energy dissipated. The energy dissipated over the time interval t is: E = P × t E = 21.390625 W × 0.15 s E = 3.20859375 J Rounding to four significant figures: b) E = 3.209 J Send me the next one 📸