91Ó°ÊÓ

: The magnetic flux initially linked with the circuit (Φ1) is 10 webers. The final magnetic flux linked with the circuit (Φ2) is 60 webers. The circuit resistance (R) is 100 ohms.

: To determine the induced current in the circuit, we need to find the change in the magnetic flux. ΔΦ = Φ2 - Φ1 ΔΦ = 60 - 10 ΔΦ = 50 webers

: According to Faraday's Law, the amount of induced electromotive force (ε) is proportional to the rate of change in magnetic flux: ε = -N * (dΦ/dt) Here, N is the number of turns in the coil, which is not given in the problem. We will assume a single-turn coil for simplicity. Now, we need to calculate dt, the time interval during which the change in magnetic flux occurs. Since neither the time interval nor the rate of change in magnetic flux is given in the problem, we will try to solve using the properties of the circuit and the provided options for the amount of induced charge.

: The induced current (I) passing through the circuit is the ratio between the induced electromotive force (ε) and the resistance (R): I = ε / R

: The amount of induced charge (Q) that flows through the circuit is the product of the induced current (I) and the time interval (dt): Q = I * dt

: We will now test each option for induced charge (Q) to see if it is consistent with our system of equations: I = ε / R Q = I * dt Option (A): Q = 0.5 coulombs - For Q = 0.5 coulombs, I * dt = 0.5 I = (0.5 / dt) Since ε = I * R, we get 0.5 / dt = ε / 100 The ratio between ε and dt remains unknown, making this solution inconclusive. Option (B): Q = 5 coulombs - For Q = 5 coulombs, I * dt = 5 I = (5 / dt) Since ε = I * R, we get 5 / dt = ε / 100 The ratio between ε and dt remains unknown, making this solution inconclusive. Option (C): Q = 50 coulombs - For Q = 50 coulombs, I * dt = 50 I = (50 / dt) Since ε = I * R, we get 50 / dt = ε / 100 The ratio between ε and dt remains unknown, making this solution inconclusive. Option (D): Q = 100 coulombs - For Q = 100 coulombs, I * dt = 100 I = (100 / dt) Since ε = I * R, we get 100 / dt = ε / 100 The ratio between ε and dt remains unknown, making this solution inconclusive. Unfortunately, the information given in the problem is not sufficient to confidently select one of the options. Further information on the time interval or rate of change in the magnetic flux is necessary for a complete solution.