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Answers
See the solution in above image.
The end points of parabola A,B are in x-direction.
As force due to a magnetic field is F = i(l×B)
So we don't need to take all angles at each point of wire, because after summation only angles in x-direction will remain.
Also the length of wire in x-direction will be calculated because it is the integral length which will experience the magnetic force.
By the above image this length is AB ie from the star point to the end point of parabola.
When y=6 ,
x²=6×6=36
x=+6 , -6
X=-6 is for point A and x = +6 Is for point B.
So poin A≡(-6,6) & B≡(6,6)
Length of AB =12
Hence force on wire
=i(l×B)
i=2A
I=12i^ Because current is in positive x direction
B= 2×10^-3 k^
F=2(12i^×2×10^-3k^)
F=48×10^-3(i×k)
F=0.048(-j^)
F=-0.048j^ = -0.05j^N
Answer:
When y=6 ,
x²=6×6=36
x=+6 , -6
X=-6 is for point A and x = +6 Is for point B.
So point A≡(-6,6) & B≡(6,6)
Length of AB =12
Hence force on wire
=i(l×B)
i=2A
I=12i^ Because current is in positive x direction
B= 2×10^-3 k^
F=2(12i^×2×10^-3k^)
F=48×10^-3(i×k)
F=0.048(-j^)
F=-0.048j^ = -0.05j^N
Explanation: