Question

)
A cycle wheel with 10 spokes each of length
0.5m long is rotated at a speed of 18 km/hr in a
plane normal to the earth's magnetic induction
of 3.6 x 10-5 T. Calculate the e.m.f. induced
between the
(i) axle and the rim of the cyclewheel.
(ii) ends of single spoke and ten spokes.​

Answer 1

Answer:

Option ii. is right. Please make me a brainlist answer

Answer 2

The induced emf between the axle and the rim of the cycle whee is $4.5\times10^{-5}\ V$.

The induced emf between the end of a single spoke and the other common end of 10 spokes is same.

Explanation:

Given that,

Length = 0.5 m

Magnetic field $B=3.6\times10^{-5}\ T$

Speed = 18 km/hr = 5 m/s

Since, The spokes have common ends, they are connected in parallel.

We need to calculate the frequency

Using formula of frequency

$f=\dfrac{v}{2\pi r}$

Put the value into the formula

$f=\dfrac{5}{2\pi\times0.5}$

$f=\dfrac{5}{\pi}$

We need to calculate the induced emf  

Using formula of emf

$\epsilon=\dfrac{d\phi}{dt}$

$\epsilon=\dfrac{d}{dt}(AB)$

$\epsilon=B(\dfrac{dA}{dt})$

$\epsilon=B(\pi r^2 f)$

Put the value into the formula

$\epsilon=3.6\times10^{-5}\times\pi\times(0.5)^2\times\dfrac{5}{\pi}$

$\epsilon= 4.5\times10^{-5}\ V$

Hence, The induced emf between the axle and the rim of the cycle whee is $4.5\times10^{-5}\ V$.

The induced emf between the end of a single spoke and the other common end of 10 spokes is same.

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Topic : induced emf

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