A conducting rod of length 2ℓ is rotating with constant angular speed ω about its perpendicular bisector. A uniform magnetic field overset arrow B exists parallel to the axis of rotation.The emf induced between two ends of the rod is:

Question

A conducting rod of length 2ℓ is rotating with constant angular speed ω about its perpendicular bisector. A uniform magnetic field overset arrow B exists parallel to the axis of rotation.The emf induced between two ends of the rod is: <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-iruvphjdn18d994l.jpg" /> (A) Bω ℓ 2 (B) (1/2)Bω ℓ 2 (C) (1/8)Bω ℓ 2 (D) Zero

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-iruvphjdn18d1u2b.jpg" /> Vx+(B ω l2/4)-(B ω l2/4)-Vy=0 ⇒ Vx-Vy=0

Q. A conducting rod of length $2 ℓ$ is rotating with constant angular speed $ω$ about its perpendicular bisector. A uniform magnetic field $B \to$ exists parallel to the axis of rotation.The emf induced between two ends of the rod is:

$B ω ℓ^{2}$

$\frac{1}{2} B ω ℓ^{2}$

$\frac{1}{8} B ω ℓ^{2}$

Zero

$V_{x} + \frac{B ω l ^{2}}{4} - \frac{B ω l ^{2}}{4} - V_{y} = 0$
$\Rightarrow V_{x} - V_{y} = 0$

Q. A conducting rod of length 2ℓ is rotating with constant angular speed ω about its perpendicular bisector. A uniform magnetic field B→ exists parallel to the axis of rotation.The emf induced between two ends of the rod is:

Bωℓ2

21​Bωℓ2

81​Bωℓ2