Test Index

CBSE Class 12 Physics 2019 Outside Delhi Set 1 Paper

© examsnet.com
Question : 15
Total: 27
Draw a labelled diagram of cyclotron. Explain its working principle. Show that cyclotron frequency is independent of the speed and radius of the orbit.
OR
(a) Derive, with the help of a diagram, the expression for the magnetic field inside a very long solenoid having n turns per unit length carrying a current I.
(b) How is a toroid different from a solenoid?
Solution:  
[Try yourself, similar to Q.no.14 in Delhi Set III]
OR
(a)
Let us consider a very long straight solenoid having ' n ' turns per unit length and carrying electric current ' T ' as shown. Let us consider a point well inside the solenoid at which the magnetic induction is to be found.
Consider a rectangular path ABCD of the line of induction such that AB=L= length of the rectangular path. The number of turns enclosed by the rectangles is nL. Hence the total electric current flowing through the rectangular path is nLI. According to Ampere's law,
∮
→
B
â‹…
→
dl
=µ0nLI .....(1)
Now for closed loop
∮
→
B
â‹…
→
dl
=
B
∫
A
→
B
â‹…
→
dl
+
C
∫
B
→
B
â‹…
→
dl
 +
D
∫
C
→
B
â‹…
→
dl
+
A
∫
D
→
B
â‹…
→
dl
As the direction of
→
dl
 and
→
B
 in path BC and AD are perpendicular
∴‌‌
C
∫
B
→
B
â‹…
→
dl
=
A
∫
D
→
B
â‹…
→
dl
=0
Near the ends of the solenoid, the lines of the field are crowded. While for rest of the space the lines are so widely spaced that the magnetic field is negligible.
∴‌‌
D
∫
C
→
B
â‹…
→
dl
=0
Thus
∮
→
B
â‹…
→
dl
=
B
∫
A
→
B
â‹…
→
dl
+0+0+0 =
B
∫
A
→
B
â‹…
→
dl
But
→
B
 and
→
dl
 are in the same direction
→
B
â‹…
→
dl
‌=B⋅dl⋅cos‌0∘=B⋅dl
∮
→
B
â‹…
→
dl
‌=‌
B
≡
A
⋅Bdl=B‌
B
≡
A
â‹…dl=BL .....(2)
From equation (1) and (2) we get
BL‌=µ0nLI
B‌=µ0nI
(b) A toroid can be viewed as a solenoid which has been bent into a circular shape to close on itself.
© examsnet.com
Go to Question:
Prev Question
Next Question