Question

A $10\text{m}$ wide spacecraft moves through the interstellar space at a speed $3\times {10}^7{\text{ms}}^{-1}.$ A magnetic field of $B=3\times {10}^{-10}\text{T}$ exists in the space in a direction perpendicular to the spacecraft motion. Treating the spacecraft as a conductor, find the emf induced across its width.

• A. $0.5\text{V}$
• B. $0.09\text{V}$
• C. $1\text{V}$
• D. $2.05\text{V}$

Answer 1

The correct option is B $0.09\text{V}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Given,
$l=10\text{m};v=3\times {10}^7{\text{ms}}^{-1};B=3\times {10}^{-10}\text{T}$

Wide spacecraft can be treated as a single conductor moving in a magnetic field.

Therefore, induced emf across its width is,

$E=Bvl$

$=3\times {10}^{-10}\times 3\times {10}^7\times 10$

$E=9\times {10}^{-2}\text{V}=0.09\text{V}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.