A ring of radius (R) carries a linear charge density ($\lambda$). It is rotating with angular speed ($\omega$). What is the magnetic field at the centre?
Discussion:
Linear charge density $$ \lambda=\frac{Q}{2\pi R}
$$
When the ring is rotated about the axis, the motion of the electrons in a circular orbit is equivalent to a current carrying loop.
Current $$ I=\frac{Q}{T}=\frac{Q\omega}{2\pi}$$
since Time period (T=2\pi/\omega).
Now, magnetic field around the centre of a current carrying loop is given by $$ B=\mu_0I/2R$$
Putting the value of (I) in the above equation, we get
$$ B=\frac{\mu_0\omega}{2}.\frac{Q}{2\pi R}
$$$$ \Rightarrow B=\frac{\mu_0\lambda\omega}{2}
$$
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
