An emf of 0.45V is induced between the ends of a metal bar moving through a magnetic field of 0.22 T. What field strength would be needed on emf of 1.5 V between the ends of the bar, assuming that all other factors remain the same? (Ans; 0.73 T)


Data Given:

1st emf = `\Ɛ_1` = 0.45 V

1st Magnetic Field = `\B_1` = 0.22 T

2nd emf = `\Ɛ_2` = 1.5 V



To Find:

2nd Magnetic Field = `\B_2` = ?


Solution:

Using the following relations

`\Ɛ_1` = `\B_1` V L sin θ -----------(1)

`\Ɛ_2` = `\B_2` V L sin θ ------------(2)

As given all the other factors will remain the same, values V, L, and θ values will remain the same for both equations (1) and (2).

Dividing the equation (2) by (1)

`\frac {Ɛ_2}{Ɛ_1}` = `\frac {\B_2 V L sin θ}{\B_1 V L sin θ }`

`\frac {Ɛ_2}{Ɛ_1}` = `\frac {B_2}{B_1 }`

or

`\B_2` = `\frac {B_1Ɛ_2}{Ɛ_1 }`

by putting values

`\B_2` = `\frac {0.22 T ｘ1.5 V}{0.45 V }`

`\B_2` = `\frac {0.33 T V}{0.45 V }`

`\B_2` = 0.733 T  ------------Ans.



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