The figure below shows the path of an proton in a region of uniform magnetic fie
ID: 1634445 • Letter: T
Question
The figure below shows the path of an proton in a region of uniform magnetic field. The path consists of two straight sections, each between a pair of uniformly charged parallel plates, and two half circles. When the proton is outside the plates, it sees only a magnetic field which exerts a force on the proton to make it travel around a circle. When the proton is between the plates, it sees both an electric and magnetic field, which both exert forces on the proton that cancel, so the proton travels along a straight line. Assume that the length L shown in the figure is known. B = 2m_P Delta V/eLd B = mx/qR B = Squareroot m_P Delta V/eLd B = 2m_P v/eL.Explanation / Answer
given that the particle is proton,
so charge = e
mass = m
let magentic field be B
then force on the proton while it is just experienceing magnetic field , F = evB
here v is velocity of motion of proton
but from newtons second law, this force is equal to centripital force
mv^2/r = evB [ where r is radius of the circle in which the proton is moving at the D's]
so, r = mv/eB
but L = 2r( from the diagram)
so, L = 2mv/eB
hence, B = 2mv/eL ( hence option 4. )