3.11.1 TORQUE ON A CURRENT LOOP PLACED IN A UNIFORM ... · 12/08/2019 · 3.11.1 torque on a...
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3.11.1 TORQUE ON A CURRENT LOOP PLACED IN A UNIFORM MAGNETIC FIELD 12TH PHYSICS - HOTS SPOT & IMPORTANT QUESTION STUDY MATERIAL PREPARED BY Mr.D.VIJAY VIJAYAN,M.Sc,B.Ed,CLP. Cont: 80727 44166 MODERNTUITION CENTRE,THURAIPAKKAM PTC/SEMMENCHERRY (OMR)CHENNAI. Page 1 01. Derive an expression of torque acting on a rectangular current loop place in a uniform magnetic field whose plane is parallel to the magnetic field or unit vector normal to the magnetic field. Let’s consider the plane of a rectangular current loop PQRS placed parallel to the uniform magnetic field ‘B’. a,b and - length, breath and unit normal vector of the loop PQRS Let the current I passing through the loop along PQRS as shown in fig. The net force acting on a loop is zero but it there will be an influence of torque which makes the loop rotates. Calculation of net Lorenz force Let the plane of the loop PQRS lying on the plane, where acting perpendicular to the magnetic field. Divide the loop PQRS into four parts PQ, QR, RS and SP (i) Force on section PQ ̂ ̂ ( ̂̂ ) (ii) The force on section QR ̂ ̂ (̂̂) (iii) The force on section RS ̂ ̂ ( ̂̂ ) (iv) The force on section SP ̂ ̂ (̂̂) The net force on the rectangular loop is Here net force is zero; therefore there will not be any translational motion of the loop that is the loop will not undergo any linear motion in the field instead of it, they cause torque on the loop. Net torque on the loop about the axis passing through the loop lie along the plane of the loop as shown in figure is ∑ ∑ ( ) ( ) ( ) ( ) To find ( ) To find ( ) Q P axis 2 ̂ ( ) sin ̂ 2 ̂ sin 9 0 ̂ ( ) 2 ̂ R S axis 2 ̂ ̂ -̂ ( ) sin ̂ 2 ̂ sin 9 0 ̂ ( ) 2 ̂ www.Padasalai.O www.Padasalai.O www.Padasalai.O www.Padasalai.O www.Padasalai g www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai g www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai g www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai g www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai g www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai g www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai g www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai g www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai g www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai g www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai g www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai g www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai www.Padasalai.O www.Padasalai.O www.Padasalai.O www.Padasalai.O www.Padasalai.O www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.O www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.O www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.O www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.O www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.O www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.O www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.O www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.O www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.O www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.O www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.O www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.Org www.Padasalai.O www.Padasalai.Net www.TrbTnpsc.com
Transcript of 3.11.1 TORQUE ON A CURRENT LOOP PLACED IN A UNIFORM ... · 12/08/2019 · 3.11.1 torque on a...
3.11.1 TORQUE ON A CURRENT LOOP PLACED IN A UNIFORM MAGNETIC FIELD
12TH PHYSICS - HOTS SPOT & IMPORTANT QUESTION
STUDY MATERIAL PREPARED BY Mr.D.VIJAY VIJAYAN,M.Sc,B.Ed,CLP. Cont: 80727 44166 MODERNTUITION CENTRE,THURAIPAKKAM PTC/SEMMENCHERRY (OMR)CHENNAI. Page 1
01. Derive an expression of torque acting on a rectangular current loop place in a uniform magnetic field
whose plane is parallel to the magnetic field or unit vector normal to the magnetic field.
Let’s consider the plane of a rectangular current loop PQRS placed parallel to the uniform magnetic field ‘B’.
a,b and - length, breath and unit normal vector of the loop PQRS
Let the current I passing through the loop along PQRS as shown in fig. The net force acting on a loop is zero but it there
will be an influence of torque which makes the loop rotates.
Calculation of net Lorenz force
Let the plane of the loop PQRS lying on the plane,
where acting perpendicular to the magnetic field.
Divide the loop PQRS into four parts PQ, QR, RS and SP
(i) Force on section PQ
( )
(ii) The force on section QR
( )
(iii) The force on section RS
( )
(iv) The force on section SP
( )
The net force on the rectangular loop is
Here net force is zero; therefore there will not be any translational motion of the loop that is the loop will not
undergo any linear motion in the field instead of it, they cause torque on the loop.
Net torque on the loop about the axis passing through the loop lie along the plane of the loop as shown in figure is
∑ ∑
( ) ( ) ( ) ( )
To find ( ) To find ( )
Q
P axis
𝑟 𝑏
2𝑖
(𝑟 𝑋�� )𝑃𝑄 𝑟 �� sin𝜃 𝑗
𝑏
2𝑖 𝐼𝑎𝐵�� sin 9 0 𝑗
(𝑟 𝑋�� )𝑃𝑄 𝑏
2𝐼𝑎𝐵𝑗
R
S
axis
𝑟 𝑏
2𝑖
𝑗
-𝑗
(𝑟 𝑋�� )𝑅𝑆 𝑟 �� sin𝜃 𝑗
𝑏
2𝑖 𝐼𝑎𝐵�� sin 9 0 𝑗
(𝑟 𝑋�� )𝑅𝑆 𝑏
2𝐼𝑎𝐵𝑗
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3.11.1 TORQUE ON A CURRENT LOOP PLACED IN A UNIFORM MAGNETIC FIELD
12TH PHYSICS - HOTS SPOT & IMPORTANT QUESTION
STUDY MATERIAL PREPARED BY Mr.D.VIJAY VIJAYAN,M.Sc,B.Ed,CLP. Cont: 80727 44166 MODERNTUITION CENTRE,THURAIPAKKAM PTC/SEMMENCHERRY (OMR)CHENNAI. Page 2
𝑙 𝑄𝑅 𝑄𝑂 𝑂𝑅
𝑏 cos 𝜋
2 𝜃 𝑖 𝑏 sin
𝜋
2 𝜃 ( ��)
𝑙 𝑏 sin𝜃 𝑖 𝑏 cos𝜃 �� 𝑎𝑛𝑑 �� 𝐵𝑖
��𝑄𝑅 𝐼𝑙 𝑋 �� 𝐼(𝑏 sin𝜃 𝑖 𝑏 cos𝜃 �� )𝑋 𝐵𝑖
��𝑄𝑅 𝐼𝑏𝐵 sin𝜃 (𝑖 𝑋 𝑖 ) 𝐼𝑏𝐵 cos𝜃 (�� 𝑋 𝑖 )
��𝑄𝑅 𝐼𝑏𝐵 cos𝜃 𝑗 (∵ 𝑖 𝑋 𝑖 )
��
��
𝑖 𝑖
𝐼 ��
P
𝑙-
S
𝑙
𝜋
2 𝜃
𝜋
2 𝜃
𝜋
2 𝜃
B
b
𝑙 𝑆𝑃 𝑆𝐴 𝐴𝑃
𝑏 cos 𝜋
2 𝜃 ( 𝑖) 𝑏 sin
𝜋
2 𝜃 (��)
𝑙 𝑏 sin𝜃 𝑖 𝑏 cos𝜃 �� 𝑎𝑛𝑑 �� 𝐵𝑖
��𝑆𝑃 𝐼𝑙 𝑋 �� 𝐼(𝑏 sin𝜃 𝑖 𝑏 cos𝜃 �� )𝑋 𝐵𝑖
��𝑆𝑃 𝐼𝑏𝐵 sin𝜃 (𝑖 𝑋 𝑖 ) 𝐼𝑏𝐵 cos𝜃 (�� 𝑋 𝑖 )
��𝑆𝑃 𝐼𝑏𝐵 cos𝜃 𝑗 (∵ 𝑖 𝑋 𝑖 )
( ) ( )
2
2
When the loop starts rotating about y axis ( i,e )due to this torque, the magnetic field no longer act parallel to the
plane.
02. Derive an expression of torque acting on a rectangular current loop
place in a uniform magnetic field whose plane inclined to the magnetic field
about an angle ‘’ or unit normal vector makes an angle ‘’ to the magnetic field B.
Let consider the plane of the loop PQRS placed in a magnetic field
with an angle of inclined ‘’
(i) The force on section PQ
( )
(iii) The force on section RS
( )
(ii) The force on section QR (iv) The force on section SP
A
𝜋
𝜃
𝜃
Q O A
magnetic line R
Horizontal Component of 𝑙
vert
ical
co
mp
on
ent
of
𝑙
��
𝜃
𝑖 𝑖
��
��
b
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3.11.1 TORQUE ON A CURRENT LOOP PLACED IN A UNIFORM MAGNETIC FIELD
12TH PHYSICS - HOTS SPOT & IMPORTANT QUESTION
STUDY MATERIAL PREPARED BY Mr.D.VIJAY VIJAYAN,M.Sc,B.Ed,CLP. Cont: 80727 44166 MODERNTUITION CENTRE,THURAIPAKKAM PTC/SEMMENCHERRY (OMR)CHENNAI. Page 3
The net force on the rectangular loop is
cos cos
Here net force is zero; therefore there will not be any translational motion of the loop that is the loop will not
undergo any linear motion in the field instead of it, they cause torque on the loop.
Having same action of point and acting equally in opposite direction and they cancelled each other, but it
will not make any deformation of the loop due to the rigidity of the loop material. Hence no torque produces by them.
The torque is produce by the forces
[
cos
( )
sin
] [
cos
( )
sin
( )] [ ]
2{ sin ( ) cos ( )}
2{ sin ( ) cos ( )}
2{ sin sin }
2*2 sin +
sin sin
Torque acting along positive y axis and the loop rotate about y axis.
If the current flow along the loop rotate in clockwise direction and if it flows along , the
loop rotate in anticlockwise direction.
Comparison of two cases ( )
Net force Zero Zero
Torque maximum
( )
varying from maximum to minimum sin , variable
��𝑛𝑒𝑡
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