Question

magnetic field = 0.678 t
wire length =
relative speed = 16.715 m/s
emf = 55.3 v
64 m
91.2 m
4.88 m
1.95 m
magnetic field = 0.667 t
wire length =
relative speed = 28.129 m/s
emf = 36.5 v
1.95 m
64 m
91.2 m
4.88 m

Explanation:

Step1: Recall the formula for EMF

The formula for the electromotive force (EMF) induced in a moving wire in a magnetic field is \( \mathcal{E}=BLv\), where \( \mathcal{E}\) is the EMF, \( B\) is the magnetic field, \( L\) is the length of the wire, and \( v\) is the relative speed. We need to solve for \( L\), so \( L = \frac{\mathcal{E}}{Bv}\).

Step2: Substitute values for the first set of data

Given \( \mathcal{E}=55.3\space V\), \( B = 0.678\space T\), \( v=16.715\space m/s\).
\( L=\frac{55.3}{0.678\times16.715}\)
First, calculate \( 0.678\times16.715 = 11.33277\).
Then \( L=\frac{55.3}{11.33277}\approx4.88\space m\).

Step3: Substitute values for the second set of data

Given \( \mathcal{E}=36.5\space V\), \( B = 0.667\space T\), \( v = 28.129\space m/s\).
\( L=\frac{36.5}{0.667\times28.129}\)
First, calculate \( 0.667\times28.129=18.762043\).
Then \( L=\frac{36.5}{18.762043}\approx1.95\space m\).

Answer:

For the first set of data: \(4.88\space m\).
For the second set of data: \(1.95\space m\).