Question

The earth's magnetic field strength is$5.0\times {10}^{-5}\text{T}$ . How fast would you have to drive your car to create a $1.0\text{V}$motional emf along your $1.0-\text{m}$-tall radio antenna? Assume that the motion of the antenna is perpendicular to$\overrightarrow{B}$ .

Short answer

The speed of the car is$2000\text{m}/\text{s}$

Step-by-step solution

Step 1. Given information

Earth's magnetic field strength, $B=5\times {10}^{-5}\text{T}$

Length of antenna,$l=1.0\text{m}$

The motional emf,$e=1V$

Step 2. Explanation

The motional emf

$\begin{array}{l}e=l(v\times B)\\ e=l\left(vB\sin \right)\\ e=lvB\\ \left(1\text{\hspace{0.05em}V}\right)=\left(1\text{\hspace{0.05em}m}\right)v\left(5\times {10}^{-4}\text{\hspace{0.05em}T}\right)\\ v=2000\text{m}/\text{s}\end{array}$

The speed of the car is$2000\text{m}/\text{s}$