Question

Particle accelerators, such as the Large Hadron Collider, use magnetic fields to steer charged particles around a ring Consider a proton ring with 36 identical bending magnets connected by straight segments. The protons move along a 1.0-m-long circular arc as they pass through each magnet. Part A What magnetic field strength is needed in each magnet to steer protons around the ring with a speed of 2.0 x 10 m/s? Assume that the field is uniform inside the magnet, zero outside. Express your answer with the appropriate units

Answer 1

Answer:

$\beta= 3.49x10^{-8}T$

Explanation:

The magnetic field can be find using the equation

$m*v^2/r=q*v*\beta$

You can cancel a element of v'

$m*v/r=q*\beta$

$C=36*1m=2\pi*r$

$r=\frac{36}{2\pi } =5.7295m$

Solve to magnetic field

$\beta=\frac{m*v^2}{r*q}$

The charge and mass of the proton are:

$m_p=1.6x10^{27}kg$, $q_p=1.6x10^{-19}C$

Replacing numeric

$\beta=\frac{1.6x10^{-27}kg*2x10m/s}{1.6x10^{-19}C*5.73m}$

$\beta= 3.49x10^{-8}T$