in this example we are given that a charge
4 micro coulomb enters in a region of uniform
magnetic field with a velocity 4 i-cap plus
7 j-cap meters per second.
and it experiences a force 5 i-cap minus c
j-cap newton and we are required to find the
value of c. so here we know that.
we can write as we know.
magnetic force.
is.
always, perpendicular to.
velocity of charge particle. as we know the
value of magnetic force vector is given as
q multiplied by v cross b. so in this situation
the direction of force vector is normal to
both velocity vector and magnetic field vector.
so we can write as f vector is perpendicular
to v vector this implies.
the dot product of the force vector and the
velocity vector must be equal to zero.
so we substitute the values it’ll be 5 i-cap
minus c j-cap.
dot product with 4 i-cap plus 7 j cap, which
should be equal to zero. on simplifying here
we are getting it to be 20 minus 7 c is zero.
or we can see the value of c we are getting
is 20 by 7 that will be the answer to this
problem.
