An insulated square frame ABCD of side a is able to rotate about one of its sides taken as +z axis. A magnetic field B is present in the region given by 
= B 0 
. A small block of mass m and charge q movable along side CB is initially near C, when the frame lies in the x-z plane. Now the frame is given an angular velocity ω about the z-axis. The whole system lies in gravity-free space. If after time t the block reaches B, find B 0 in terms of t.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. The block moves with speed v = ω a in the x-y plane.
The velocity of the block, when the frame has rotated through an angle θ = ω t,
= ω a( –sin θ 
+ cos θ 
) + v z 
Force on the block,
F = 
× 
= [ ω a(– sin θ 
+ cos θ 
) + v z 
] × B 0 
Force in z-direction
= ω aB 0 (– 
) sin θ
Acceleration block,
a z = 
(– 
)
or 
= – 
sin ω t 
or v z = – 
ω t dt = – 
(1 – cos ω t)
= – 
(1 – cos ω t)
or dz = – 
z = – 
= – 
When the block reaches B, z = – a
or – a = – 
or B 0 = 
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems