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AP Physics C: E&M
13.3 Induced Currents and Magnetic Forces
13.2 Electromagnetic Induction
13.1 Magnetic Flux
AdvancedMCQGraphicalMathematicalConceptual23.1k
Induced current I(t) as a function of time t for the loop transiting the magnetic field.
Induced current I(t) as a function of time t for the loop transiting the magnetic field.
A flat rectangular loop of wire with length \(L\), width \(w\), and resistance \(R\) moves in the \(+x\)-direction at constant speed \(v_0\). At time \(t = 0\), the front edge of the loop enters a magnetic field region extending from \(x = 0\) to \(x = 2L\). Within this region, the magnetic field is directed into the page with spatially varying magnitude \(B(x) = B_0 \dfrac{x}{L}\), where \(B_0\) is a positive constant, and \(B = 0\) elsewhere. Defining counterclockwise current as positive, the induced current \(I(t)\) as a function of time increases linearly from \(0\) to \(+I_0\) for \(0 \le t \le T\), remains constant at \(+I_0\) for \(T \le t \le 2T\), and jumps to \(-I_0\) at \(t = 2T\) before rising linearly to \(0\) at \(t = 3T\), where \(T = \dfrac{L}{v_0}\) and \(I_0 = \dfrac{B_0 w v_0}{R}\). Which of the following claims correctly explains the physical origin of a feature in the \(I(t)\) graph?

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