A conducting ring of radius r is rolling without slipping with a constant angular velocity ω (figure). If the magnetic field strength is B and is directed into the page then the emf induced across PQ is

Question

A conducting ring of radius r is rolling without slipping with a constant angular velocity ω (figure). If the magnetic field strength is B and is directed into the page then the emf induced across PQ is (A) Bω r2 (B) (Bω r2/2) (C) 4 B ω r2 (D) (π2 r2 Bω/8)

Tardigrade Admin · Accepted Answer

|E| = Magnitude of induced emf = (Bl2/2) ω, l = √2 r E = (B(2r2) ω/2) = B ω r2

Q. A conducting ring of radius $r$ is rolling without slipping with a constant angular velocity $ω$ (figure). If the magnetic field strength is $B$ and is directed into the page then the emf induced across $PQ$ is

$B ω r^{2}$

$\frac{B ω r ^{2}}{2}$

$4 B ω r^{2}$

$\frac{π ^{2} r ^{2} B ω}{8}$

$∣ E ∣ =$ Magnitude of induced emf
$= \frac{B l ^{2}}{2} ω, l = 2 r$
$E = \frac{B ( 2 r ^{2} ) ω}{2} = B ω r^{2}$

Q. A conducting ring of radius r is rolling without slipping with a constant angular velocity ω (figure). If the magnetic field strength is B and is directed into the page then the emf induced across PQ is

Bωr2

2Bωr2​

4Bωr2

8π2r2Bω​