A square conducting frame of side a is coplanar with a very long straight wire carrying current I. Its nearest edge is a distance x from the wire. The frame moves away from the wire at speed v. To what function of x is the induced emf proportional? [Image]
Options

Question

A square conducting frame of side a is coplanar with a very long straight wire carrying current I. Its nearest edge is a distance x from the wire. The frame moves away from the wire at speed v. To what function of x is the induced emf proportional? [Image]

Options

G1 Physics · Accepted Answer

Step 1: The infinite straight wire produces a field B(r) = μ₀I/(2πr). Step 2: The rectangular frame moves sideways at speed v, so the changing net flux is Φ = (μ₀Ia/(2π)) ln((x+a)/x). Step 3: Differentiate: |ε| = (μ₀Iav/(2π))[1/x − 1/(x+a)] = μ₀Ia²v/[2πx(x+a)]. The intended option is D; check OCR expression against PDF. Final answer: (D) 1/[(2x − a)(2x + a)].