3. Figure (34-E17) shows a convex lens of focal length
12 cm lying in a uniform magnetic field B of magnitude
1.2 T parallel to its principal axis. A particle having a
charge 2:0 x 10-C and mass 2:0 x 10 - kg is projected
perpendicular to the plane of the diagram with a speed
of 4:8 ms. The particle moves along a circle with its
centre on the principal axis at a distance of 18 cm from
the lens. Show that the image of the particle goes along
a circle and find the radius of that circle.
Answers
Answer:
Explanation:
ANSWER
According to the given criteria,
Focal length of the convex lens, f=12cm
Uniform magnetic field, B=1.2T
Charge on the particle, q=2.0×10
−3
C
Mass of the particle, m=2.0×10
−6
kg
Speed of the particle, v=4.8m/s
The distance of the particle from the lens, object distance, u=−18cm
As particle is projected perpendicular to the plane.
Let the radius of the circle on which the object is moving be r
We know,
r=
qB
mv
⟹r=
2.0×10
−3
×1.2
2.0×10
−6
×4.8
⟹r=4×10
−3
m=0.4cm
Now applying the lens formula, we get
f
1
=
v
1
−
u
1
⟹
12
1
=
v
1
−
(−18)
1
⟹
v
1
=
12
1
−
18
1
⟹
v
1
=
36
3−2
⟹v=36cm
Let the radius of the circular path of image be r
′
So magnification, m=−
u
v
=
r
r
′
⟹−
(−18)
36
=
0.4
r
′
⟹r
′
=
18
36×0.4
⟹r
′
=0.8cm
So the radius of the circular path in which the image movesis 0.8 cm.