Answer to Question #197998 in Electricity and Magnetism for Gatter

Question

Suddenly uniform magnetic field B₀ (-k) is applied in the circular gravity free region having radius 4a. Initially field was zero and charge (q, m) was at rest at (a, 0). Now once field is setup find the radius, of circular path (in meter) Given : a = 4.00 m. 

In the answer E.2(pi)a = B.(pi)a² is taken. imagining a circle with centre origin. My question is why not take any arbitrary circle with an arbitrary centre which pases through (a,0)

Answer 1

Charge is rest on at point Phaving coordinate (a,0) and magnetic field is (-z) direction. When charge is moving in circular path it has 2 forces; magnetic and centrifugal forces

$F_{m}=F_{centri}$

$qvB= \frac{mv^2}{r}$

$r= \frac{mv}{qB}$

r is fixed, so we can not take any arbitrary circle with any arbitrary radious $r \propto mv,r \propto \frac{1}{qB}$

The value of r is always fixed.

Charge is traveling in a circular direction with centrifugal force and magnetic force balancing each other such that the charge molecule is radious. Furthermore, since the center of charge of a particle is set, it cannot be random.

Proportional to the multiplication of (mv) mass and velocity and, conversely, proportional to the multiplication of (qB) charge and field