What magnetic field strength is needed in each magnet to steer protons around the ring with a speed of 4.5 × 107 m/s? Assume that the field is uniform inside the magnet, zero outside.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

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 3.5m long circular arc as they pass through each magnet.

What magnetic field strength is needed in each magnet to steer protons around the ring with a speed of 4.5×10⁷ m/s? Assume that the field is uniform inside the magnet, zero outside.

Given Information:

Radius = r = 36*3.5/2π = 20.05 m

Speed = v = 4.5×10⁷ m/s

Required Information:

Magnetic field = B = ?

Magnetic field = 23.35 mT

Explanation:

The force acting on the protons due to magnetic field is given by

F = qvB

Since the protons are moving around a circular ring, the corresponding centripetal force is given by

F = mv²/r

Equating the both forces

qvB = mv²/r

qB = mv/r

B = mv/rq

Where m is the mass of proton (1.67×10⁻²⁷ kg), v is the speed of proton and q is the charge on proton (1.609×10⁻¹⁹ C)

Therefore, the magnetic field is

B = (1.67×10⁻²⁷*4.5×10⁷)/(20*1.609×10⁻¹⁹)

B = 0.02335 T

or

B = 23.35 mT

float.

archimedes' principle

denser than water sinks in water.

denser than mercury would sink in it

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y