A simple Pendulum with a charged bob is oscillating as shown in figure. Time period of oscillation is and the angular amplitude is . If a uniform magnetic field perpendicular to the plane of oscillation is switched on, then
will decrease but will remain constant.
will remain constant but will decrease.
Both and will remain the same.
Both and will decrease.
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*
or_italics_
**bold**
or__bold__
paragraph 1
paragraph 2
[example link](https://brilliant.org)
> This is a quote
\(
...\)
or\[
...\]
to ensure proper formatting.2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
Comments
unrelated. but I love your microsoft paint skills
Log in to reply
why unrelated??....but i too appreciate his skill in "painting"....:)....but a suggestion to him::: he could have used "text" option to write the letter "B" in ms. paint.....:-)
Log in to reply
hmm... next tym i will!!! :P
:P LOL!!!
hahaha but I don't think that helped him much!! I think the answer's (e)
Log in to reply
LOL!!
If you consider in terms of 'energy consevation', work done by 'magnetic field' is 0. Hence, θ remains same and so or more time also.
Since, the charged particle is undergoing a periodic oscillation it will be produce only electric field as the displacement is zero after 1 time period!!! Thus, electric field will be opposed by magnetic field by Lenz's law and Lorentz force concept: lets see how.... F=q.E+(-q.vxB) Now see the net force acting on the charged particle is getting reduced by damping force from the magnetic field!!! So, it will oscillate only to balance tension of the string with perpendicular gravitational force acting on it!!! My idea that time period T of oscillation will decrease but \theta\ will remain constant!!! And moreover vXB is maximum on account that B is perpendicular to the plane of oscillation!! So, it is option a)!!!
Log in to reply
Oscillating charge produces electric field which in turn produces oscillating magnetic field which shoud be true according to you, sir. But one thing to note is that the charges are in 'constantly accelerated' motion, which in this case is equal to 0.
I guess (c) is correct. Is it right?
Log in to reply
yes bt how?
Log in to reply
Since the restoring force which is mg sinθ ('θ' as depicted in your diagram) remains the same so will ω i.e. angular frequency and so will T. Using energy conservation θ will also remain same since work done by magnetic force is zero.
(c) is the correct option... I need explanation!!