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A insulated square frame ABCD of side a ...

A insulated square frame `ABCD` of side a is able to rotate about one of its side taken as positive `z`-axis. A magnetic field `B` is present in the region given by `vecB=B_(0)hatj`. A small block of mass `m` and charge `q` movable along side `CB` is initially near `C`, when frame lies in `x-z` plane. Now, frame is rotated by constant angular velocity `omega` about `z`-axis. Whole system lies in gravity free space. If after time `t` block reaches point `B`, find `B_(0)` in terms of `t`.

Text Solution

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Block moves with speed
`v=omega a ` in `x-y` plane
Velocity of block, when frame has rotated through angle `theta=omegat`
`vecv=omega a (-sinthetahati+costhetahatj)+v_(z)hatk`
Force on block `F=qvecvxxvecB=[omega a(-sinthetahati+costhetahatj)+v_(z)hatk]xxB_(0)hatj`
Force in `z`-direction `=q omega a B_(0)(-hatk)sintheta`
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