C4. (2 points) A long straight wire is in the same plain as a rectangular conduc

Question

C4. (2 points) A long straight wire is in the same plain as a rectangular conducting loop. The wire carries a constant current, I. Which one of the following statements is true if the wire is suddenly moved towards the loop? A) There will be no induced emf and no induced current B) There will be an induced emf, but no induced current. C) There will be an induced current that is clockwise around the loop. D) There will be an induced current that is counterclockwise around the loop. E) There will be an induced electric field that is clockwise around the loop.

Explanation / Answer

let length of the loop parallel to the wire be L and width be w.

let initial distance between the wire and the lower side of the loop be h.

consider a small strip of width dx at a distance of x from the wire and parallel to wire.

magnetic field due to wire at this point=mu*I/(2*pi*x)

magnetic flux=magnetic field*area

=mu*I*L*dx/(2*pi*x)

total flux=integral of mu*I*L*dx/(2*pi*x) from x=h to x=h+w

so total flux=(mu*I*L/(2*pi))*ln((w+h)/h)

emf induced=time rate of change of flux

as wire moves towards the loop, h decreases.

and the ln((w+h)/h) value increases

so magnetic flux linking the loop increases.

due to change in magnetic flux, there will be an induced emf and hence an induced current

using lenz’s law, induced current will be such that it will oppose the original magnetic flux.

hence induced current will be in anti-clockwise direction.

hence option D is correct.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.