in this example we are given that a beam of
protons with velocity 4 into 10 to power 5
meters per second, enters a region of uniform
magnetic field. of zero point 3 tesla at an
angle 60 degree to direction of magnetic field.
we are required to find the radius and pitch
of helical path followed by particle. we know
well that whenever a particle enters in the
region of magnetic field. at some angle to
it, it follows a helical path. and in this
situation for the helical path. the radius
of helix is given by. m v sine theta by q-b.
which can be directly calculated here as the
mass of particles we need to consider that
protons this is 1 point 6 7 into 10 to power
minus 27. multiplied by the speed is 4 into
10 to power 5. multiplied by here theta we
are given as 60 degree. so sine 60 will be
root 3 by 2. divided by charge of particle
is 1 point 6 into 10 to power minus 19 multiplied
by the magnetic field is zero point 3 tesla.
on simplifying we’ll get the value is 1
point 2 into 10 to power minus. 2 meter, that
will be the answer to. the radius of this
helical path. and if we wish to find out the
pitch of helix which is the distance covered
by the particle during one revolution from
the starting point. this pitch of helix we
know it is given by 2 pie m v coz theta by
q-b. if we substitute the values it’ll be,
2 into 3 point 1 4 multiplied by. mass is
again 1 point 6 7 into ten to power minus
27 multiplied by the speed is. 4 into 10 to
power 5. and coz theta here we can write as
point 5 because theta is 60 degree, multiplied
by q-b is 1 point 6 into 10 to power minus
19 into zero point 3. if we simplify the calculation
the result will be getting is 4 point 3 7.
into 10 to power minus 2 meter that will be
the answer to the problem.
