Question

Protons with kinetic energy K emerge from an accelerator as a narrow beam. The beam is bent by a perpendicular magnetic field, so that it just misses a plane target kept at a distance l in front of the accelerator. Find the magnetic field.

Answer 1

Explanation:

It is shown that

Proton’s kinetic energy = K

From the accelerator, the target’s distance = l

So, the circular orbit’s radius≤l

According to the provided information, by a perpendicular magnetic field, the beam is set.

It is known that

r = mveB

The given equation can be written as:

l = mpveB      (As r=l)….(i)

Here,

• mp is the mass of a proton
• e is the charge
• v is the velocity
• B is the magnetic field

⇒ v = 2Kmp

In equation (i), when the value of v is substituted, we obtain:

l = 2Kmpel

Answer 2

Explanation:

It is shown that

Proton’s kinetic energy = K

From the accelerator, the target’s distance = l

So, the circular orbit’s radius≤l

According to the provided information, by a perpendicular magnetic field, the beam is set.

It is known that

r = mveB

The given equation can be written as:

l = mpveB      (As r=l)….(i)

Here,

mp is the mass of a proton

e is the charge

v is the velocity

B is the magnetic field

⇒ v = 2Kmp

In equation (i), when the value of v is substituted, we obtain:

l = 2Kmpel