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Question


The figure shows a metallic solid block, placed in a way so that its faces are parallel to the coordinate axes. Edge lengths along axis x,y and z are a,b and c respectively. The block is in a region of uniform magnetic field of magnitude 30 mT. One of the edge length of the block is 25 cm. The block is moved at 4 m/s parallel to each axis and in turn, the resulting potential difference V that appears across the block is measured.
(1)When the block is moved at 4 m/s parallel to the y- axis, V=24 mV,
(2)when the block is moved at 4 m/s parallel to the z- axis V=36 mV,
(3)when the block is moved at 4 m/s parallel to the x- axis, V=0
Using the given information, correctly match the dimensions of the block in column-I with the values given in column-II.
column IColumn II(A) a(p) 20 cm(B) b(q) 24 cm(C) c(r) 25 cm(D) bca(s) 30 cm(t) 26 cm

A
Ap,Bq,Cs,Dt
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B
Aq,Bs,Ar,Dp
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C
Ar,Bs,Cp,Dq
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D
As,Bp,Cs,Dt
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Solution

The correct option is C Ar,Bs,Cp,Dq
In general emf generated,
ε=B.(l×v);
(l×v) is component of l perpendicular to v.

Since when v is along x - axis, ε=0,B must be along x - axis.

When v is along y - axis,
emf generated ε=B(cv)=24 mV (Since c swipes the defining flux)30×103×c×4=24×103c=0.2c=20 cm

When v is along z- axis
emf generated ε=B(bv)=36 mV(Since b swipes the defining flux)30×103×b×4=36×103b=0.3mb=30 cm
b=30 cm,c=20 cm and a=25 cmbca=30×2025=24 cm

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