Concept

# Problem: A (17cm X 17cm) square loop lies in the xy plane The magnetic field in this region of space is B = (0.31t i + 0.55t2 k)T where t is in seconds.1) What is the E induced loop at 0.5s2)What is the E induced loop at 1.0sExpress your answer to two significant figures and include the appropriate units.

###### FREE Expert Solution

We are dealing with induced emf.

Induced emf:

$\overline{){\mathbf{\epsilon }}{\mathbf{=}}{\mathbf{-}}\frac{\mathbf{d}{\mathbf{\varphi }}_{\mathbf{B}}}{\mathbf{d}\mathbf{t}}}$

Magnetic flux:

$\overline{){{\mathbf{\varphi }}}_{{\mathbf{B}}}{\mathbf{=}}{\mathbf{B}}{\mathbf{A}}}$

Power rule of derivation:

$\overline{)\frac{\mathbit{d}}{\mathbit{d}\mathbit{t}}\mathbf{\left(}{\mathbit{x}}^{\mathbit{n}}\mathbf{\right)}{\mathbf{=}}{\mathbit{n}}{{\mathbit{x}}}^{\mathbit{n}\mathbf{-}\mathbf{1}}}$

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###### Problem Details

A (17cm X 17cm) square loop lies in the xy plane The magnetic field in this region of space is B = (0.31t i + 0.55t2 k)T where t is in seconds.

1) What is the E induced loop at 0.5s

2)What is the E induced loop at 1.0s

Express your answer to two significant figures and include the appropriate units.