Question

magnetic field = wire length = 3.039 m relative speed = 45.266 m/s emf = 1.347 v 0.698 t 0.00373 t 0.02653 t 0.009792 t magnetic field = wire length = 6.547 m relative speed = 31.348 m/s emf = 5.445 v 0.02653 t 0.009792 t 0.00373 t 0.698 t

Explanation:

Step1: Recall the formula for motional EMF

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

Step2: Substitute the values for the first set of data

Given \( \mathcal{E}=1.347\space V\), \( L = 3.039\space m\), \( v=45.266\space m/s\).
\( B=\frac{1.347}{3.039\times45.266}\)
First, calculate \( 3.039\times45.266 = 3.039\times45+3.039\times0.266=136.755+0.808374 = 137.563374\)
Then \( B=\frac{1.347}{137.563374}\approx0.009792\space T\)

Step3: Substitute the values for the second set of data

Given \( \mathcal{E} = 5.445\space V\), \( L=6.547\space m\), \( v = 31.348\space m/s\)
\( B=\frac{5.445}{6.547\times31.348}\)
Calculate \( 6.547\times31.348=6.547\times30 + 6.547\times1.348=196.41+8.825356=205.235356\)
Then \( B=\frac{5.445}{205.235356}\approx0.02653\space T\)

Answer:

For the first problem: \(0.009792\space T\) (the fourth option). For the second problem: \(0.02653\space T\) (the first option).