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 - Physics

Sum

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.

Solution

Given:
Kinetic energy of proton = K
Distance of the target from the accelerator = l
Therefore, radius of the circular orbit ≤ l
As per the question, the beam is bent by a perpendicular magnetic field.
We know
r = (mv)/(eB)
For a proton, the above equation can be written as:
l  = (m_pv)/(eB)      (As r=l)....(i)
Here,
mp is the mass of a proton
is the velocity
is the charge
is the magnetic field
1/2 m_pv^2 = K

⇒ v= sqrt((2K)/m_p

putting the value of V in the equation (i),we get
l =( sqrt2K_mp)/(eB)

B = sqrt(2Kmp)

Concept: Force on a Moving Charge in Uniform Magnetic and Electric Fields
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 12 Magnetic Field
Q 33 | Page 232