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The fig. 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. When the motion is parallel to the y-axis, V = 24 mV; with the motion parallel to the z-axis, V = 36 mV; with the motion parallel to the x-axis, V = 0. Using the given information, correctly match the dimensions of the block with the values given,
Column – I Column – II
A) a P) 20 cm
B) b Q) 24 cm
C) c R) 25 cm
D) $\frac{bc}{a}$ S) 30 cm
T) 26 cm

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$A - R; B - S; C - P; D - T$

$A - R; B - S; C - P; D - Q$

$A - R; B - S; C - P; D - P$

$A - R; B - P; C - S; D - Q$

answer is B.

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Detailed Solution

Magnetic field is along x-axis because when the cube is moved along x-axis, there is no motional emf as $\vec{v} \times \vec{B} = 0.$ When the block is moved along y-axis, force on the electrons is in direction $- (j \times i) = k$

Therefore electric field will be created along z-axis

Now, c.v.B = 24 mV $\Rightarrow$ c = 20 cm

Similarly $bvB = 36 mV \Rightarrow b = 30 cm$

a = 25 cm

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