Twelve wires of equal lenghts (each 10 cm) are connected in the form of a skeleton cube. If the cube is moving with a velocity 0.05 `Wb//m^(2)`, find the emf induced in each arm of the cube, If the cube. If the moves perpendicular to the field, What will be the induced e.m.f. in each arm ?

Explanation

Here, `l = 10 cm = 0.1 m, upsilon = 5 m//s`,
`B = 0.05 Wb//m^(2) , e = ?`
Recollect that for generation of motional e.m.f., B, l and `upsilon` be along mutually perperdicular direction . If any or the two quantities are parallel,
`e = 0`.
In fig. Velocity of all the 12 conductors is parallel to magnetic field B, therefore, no e.m.f. is induced in any conductor.
In fig. arms AD, BC, EH and FG are parallel to velocity `(upsilon)`, So induced e.m.f. In these arms is zero. Further, arms AB, CD, EF, and GH are parallel to `vec B`. Therefore, no e.m.f. is induced in these arms.
The rest of four arms AE, BF, CG and DH are perpendicular to both `vec upsilon` and `vec B`. Therefore e.m.f. induced in each of these arms is
`e = B l upsilon = 0.05 xx 10^(-1) xx 5 = 2.5 xx 10^(-2) V`