Charge in Variable Magnetic Field - 1

Electricity and Magnetism Level 4

On a normal co-ordinate axis. A magnetic field exists given by $B=-{ B }_{ 0 } x \hat { k }$ . A point particle of charge $q$ and mass $m$ is placed at the origin and given an initial velocity $v_{0}$ in the positive x direction.

How will its trajectory be?

Increasing y co-ordinate ; Periodic change in x co-ordinate Repetitive Circular Spiral of decreasing radius Straight Line Spiral of increasing radius Cycloidal Any Other Increasing x co-ordinate ; Periodic change in y co-ordinate

2 solutions

Rohit Gilbert
Feb 13, 2016

Jatin sharma : check this out xD https://brilliant.org/profile/deepanshu-khqs5e/sets/deepanshus-mechanics-blasts/204698/problem/will-sliding-rod-ever-stop/?group=w1AFAqVs71C6

Oh My god xD

Jatin Sharma - 5 years, 4 months ago

Jatin Sharma
Feb 7, 2016

The solution to this doesnt need calculus See symmetry of the thing. Thus it will be the givenanswer

https://brilliant.org/problems/where-does-the-particle-stop

Jatin Sharma - 5 years, 4 months ago

send me the link of a similar problem

Rohit Gilbert - 5 years, 4 months ago

Try to solve this one!(Click this) I couldn't!

Jatin Sharma - 5 years, 4 months ago

I m still on the last one

Rohit Gilbert - 5 years, 4 months ago

@Rohit Gilbert – Dude I understood what area i have to calculate the inside of the three symmetric parabolas. Will have to use integration!!! Seriously?

Jatin Sharma - 5 years, 4 months ago

@Jatin Sharma – not really...use symmetry. i mean yes integration has to be used but its not complicated

Rohit Gilbert - 5 years, 4 months ago

@Rohit Gilbert – My comment

Jatin Sharma - 5 years, 4 months ago

Dude How did you solve the Balls in a semicircle. Its a really nice problem. Max Deflection Angle pata tha pehle se?

Jatin Sharma - 5 years, 4 months ago

i didnt remember the result...so i proved it ...but i got the ans as pi/2 actually the angle with which it should deflect once ..didnt work so i put pi instead. if the angle subtended at the centre is pi/n then the angle with which it should get deflected should be pi/2n by geometry

Rohit Gilbert - 5 years, 4 months ago

@Rohit Gilbert – i m sorry ...i did a stupid mistake ...got pi as the ans

Rohit Gilbert - 5 years, 4 months ago

https://brilliant.org/practice/combinations-level-3-4-challenges/?subtopic=counting&chapter=combinations

Rohit Gilbert - 5 years, 4 months ago

Can u elaborate. I did it using integration.

Abhi Kumbale - 4 years, 6 months ago