Question

38. ..Calc A rectangular loop of wire with a length a and width b lies in the x-y plane, as shown in Figure 20-41. Within the loop, there is a time-dependent and spatial-dependent magnetic field given by \( \vec{B}(t) = B_0[x \cos \omega t \hat{x} + y \sin \omega t \hat{z}] \) SI units Figure 20-41 Problem 38 (a) Derive an expression for the induced potential in the loop as a function of time. (b) Calculate the numerical value of the induced potential at \( t = 2.0 \) s, if \( a = 20 \) cm, \( b = 10 \) cm, and \( B_0 = 0.575 \) T/m.

          38. ..Calc A rectangular loop of wire with a length a and width b lies in the x-y plane, as shown in Figure 20-41. Within the loop, there is a time-dependent and spatial-dependent magnetic field given by \( \vec{B}(t) = B_0[x \cos \omega t \hat{x} + y \sin \omega t \hat{z}] \) SI units


Figure 20-41 Problem 38

(a) Derive an expression for the induced potential in the loop as a function of time. (b) Calculate the numerical value of the induced potential at \( t = 2.0 \) s, if \( a = 20 \) cm, \( b = 10 \) cm, and \( B_0 = 0.575 \) T/m.

38. ..Calc A rectangular loop of wire with a length a and width b lies in the x-y plane, as shown in Figure 20-41. Within the loop, there is a time-dependent and spatial-dependent magnetic field given by B⃗(t) = B0[x cosω t x̂ + y sinω t ẑ] SI units

Figure 20-41 Problem 38

(a) Derive an expression for the induced potential in the loop as a function of time. (b) Calculate the numerical value of the induced potential at t = 2.0 s, if a = 20 cm, b = 10 cm, and B0 = 0.575 T/m.

Added by William K.

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