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Magnetic field along x-axis varies accor...

Magnetic field along x-axis varies according to the relation `vec(B) = B_(0) x hat(i)`. Given a coil of area A with its axis along x-axis is connected over the top of a plastic trolly which moves along x-axis with velocity v. If the resistance of coil is R, then (at t= 0, coil is at x = 0 and `v = v_(0)`)

A

The flux linked with the coil at any position x is `B_(0)xA`

B

An observer at origin 'O' finds the induced current as `(B_(0)Av_(0))/(R)` anticlockwise it trolly moves with constant velocity `v = v_(0)`

C

If the trolly has acceleration `alpha` then the induced current as a function of time t is given as `(B_(0)A(v_(0)+alphat))/(R)` anticlockwise

D

If the trolly has acceleration `alpha` then the induced current as a function of position x is given as `(B_(0)A(sqrt(v_(0)^(2)+2 alpha x)))/(R)` anticlockwise

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`phi=vec(B).vec(A) =B_(0)xA rArr (d phi)/(dt)=B_(0)A(dx)/(dt)=B_(0)Av`
apply `e = (dphi)/(dt)`
`i=(|e|)/(R)=(B_(0)v.A)/(R)` anticlock wise
`:. v=v_(0)+alphat (B_(0)A(v_(0)+alpha t))/(R)` anticlockwise
`v^(2) =u^(2) +2 alpha x,i`
`=B_(0)A((sqrt(V_(0)^(2)+2 alpha x)))/(R)` anticlock wise.
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