A wooden stick of length 3 l is rotating about one end with constant angular velocity ω . A uniform magnetic field B is present in space, perpendicular to the rotational plane. One third of its upper end is coated with copper. What will be the potential difference between the ends of the stick?

Question

A wooden stick of length 3 l is rotating about one end with constant angular velocity ω . A uniform magnetic field B is present in space, perpendicular to the rotational plane. One third of its upper end is coated with copper. What will be the potential difference between the ends of the stick? <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-7wgkcfgc7yhuhoax.jpg" /> (A)  (9 B ω l2/2) (B)  (4 B ω l2/2) (C)  (5 B ω l2/2) (D) ( textBÏ l2/2)

Tardigrade Admin · Accepted Answer

When the rod rotates, there will be an induced current in the rod. The given situation can be treated as if a rod ‘A’ of length

'3 l'

rotating in the clockwise direction, while an other say rod ‘B’ of length

'2 l'

rotating in the anti clockwise direction with same angular speed

' ω'

.
As we know that,

e = \frac{1}{2} Bω l^{2}

For ‘A’ : For ‘B’

e_{A} = \frac{1}{2} Bω (3 l)^{2}

&

e_{B} = \frac{1}{2} B (- ω) (2 l)^{2}

Resultant induced emf will be:

e = e_{A} + e_{B} = \frac{1}{2} Bω l^{2} (9 - 4)

e = \frac{5}{2} Bω l^{2}

$\frac{9 B ω l ^{2}}{2}$

$\frac{4 B ω l ^{2}}{2}$

$\frac{5 B ω l ^{2}}{2}$

$\frac{Bω l ^{2}}{2}$

Q. A wooden stick of length 3l is rotating about one end with constant angular velocity ω . A uniform magnetic field B is present in space, perpendicular to the rotational plane. One third of its upper end is coated with copper. What will be the potential difference between the ends of the stick?

29Bωl2​

24Bωl2​

25Bωl2​

2Bωl2​

$\frac{9 B ω l ^{2}}{2}$

$\frac{4 B ω l ^{2}}{2}$

$\frac{5 B ω l ^{2}}{2}$

$\frac{Bω l ^{2}}{2}$