Question 9
(a)
State the type of field, or fields, that may cause a force to be
exerted on a particle that is
(i)
uncharged and moving, [1]
(ii)
charged and stationary, [1]
(iii)
charged and moving at right-angles to the field. [2]
(b)
A particle X has mass 3.32 × 10-26 kg and charge +1.60 × 10-19 C.
The particle is
travelling in a vacuum with speed 7.60 × 104 m s-1. It enters a region of uniform
magnetic field that is normal to the direction of travel of the particle. The
particle travels in a semicircle of diameter 12.2 cm, as shown in Fig. 6.1.
Fig. 6.1
For the uniform
magnetic field,
(i)
state its direction, [1]
(ii)
calculate the magnetic flux density. [3]
(c)
A second particle Y has mass less than that of particle X in (b)
and the same charge.
It enters the region
of uniform magnetic field in (b) with the same speed
and along the same initial path as particle X.
On Fig. 6.1, draw the
path of particle Y in the region of the magnetic field. [1]
Reference: Past Exam Paper – June 2015 Paper 41 & 43 Q6
Solution:
(a)
(i)
gravitational
{Note that a
particle will have mass and so, a gravitational force would act.}
(ii)
gravitational and electric
(iii)
magnetic, gravitational and electric
{A magnetic force
is exerted only when the particle is moving.}
(b)
(i)
out of (plane of) paper/page
{Using
Fleming’s right hand rule.}
(ii)
{Since the
particle moves in a circle, there is a centripetal force.
The
centripetal force is provided by the magnetic force.
Magnetic
force = Centripetal force
Bqv = mv2
/ r}
B = mv / qr
B = (3.32×10-26 × 7.6×104)
/ (1.6×10-19 × 6.1×10-2)
B = 0.26 T
(c)
sketch:
semicircle with diameter < 12.2 cm
{B = mv /
qr
Radius r =
mv / Bq
When the mass m is smaller, the
radius of the circular path is also smaller.}
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