Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

A wheel with 8 metallic spokes each 50cm long is rotated with the speed of 120rev/min in a plane normal to the horizontal component of the earth's magnetic field. The earth’s magnetic field at the place is 0.4G at an angle of 600. Calculate the EMF induced between the axle and the rim of the wheel. How will the value of EMF be affected if the number of spokes was increased?

Answer
VerifiedVerified
500.1k+ views
1 likes
like imagedislike image
Hint: The induced emf in a rod rotating in a magnetic field is given by E=12BωL2. First, we have to find the emf induced in one spoke of the wheel due to the magnetic field. Then we find the resultant emf of all the spokes.

Complete answer:
seo images


It is given in the question that the horizontal component of the earth’s magnetic field is making an angle of 600.
So, the component of magnetic field which is in the plane of wheel
=0.4cos600
We know that cos600=12
=0.4×12=0.2G
We know that, 1G=104T So,
B=0.2×104T
Now,
We will find the Emf by one rod,
Emf induces in a rod of length L and rotating with angular speed ωis given by the formula
E=12BωL2
Where,
ω=angular velocity of the rod
B=external magnetic field
L=length of the rod
Also,
Angular velocity is the ratio of angular displacement to time,
ω=2πnt
Substituting the value of ωin the formula we get,
E=BL2πnt
E=0.2×104×0.52×3.14×12060
On simplifying the above terms, we get
E=3.14×105V

This is the emf produced by one spoke of the wheel. All the eight spokes of the wheel are connected in parallel to each other. This is because one end of each spoke is connected to every other spoke directly and the other end of each spoke is connected to the same rim itself. So we can imagine all the spokes in which emf is induced to be parallel with each other. We know that, if n number of cells are connected in parallel with each other then the net emf remains the same. So, no change in emf will remain unchanged on increasing the spokes in the wheel.

Note:
The rotating rods can be considered as a cell and all the cells will have the same polarity because all the rods are rotating in the same sense. To solve these kinds of questions, you have to picturise the given information and clearly understand the direction of the magnetic field.
Latest Vedantu courses for you
Grade 9 | CBSE | SCHOOL | English
Vedantu 9 CBSE Pro Course - (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
Social scienceSocial science
BiologyBiology
ChemistryChemistry
EnglishEnglish
MathsMaths
₹38,500 (9% Off)
₹35,000 per year
Select and buy