Calculating Induced EMF from AM Radio Broadcast and Dipole Antenna

[cmerickson21]

Homework Statement

An AM Radio station broadcasts isotropically(equally in all directions) with an average power of 4.00kW. A dipole receiving antenna 65.0cm long is at a location 4.00 mi from the transmitter. Compute the amplitude of the emf that is induced by this signal between the ends of the receiving antenna.

Homework Equations

$$P$$$$_{avg}$$=S$$_{}avg$$A
E$$_{max}$$=$$\sqrt{\mu_{\circ}$$cP$$_{avg}$$/2$$\pi$$r^2}
B$$_{max}$$=$$\frac{E_{max}}{C}$$

The Attempt at a Solution

Used the avg power to find the E$$_{max}$$ to be .0058V/M. tHen used this to find the B$$_{max}$$ to be 1.9305*10^-11T. I am not sure how to calculate the emf from this.

 

[Redbelly98]

Use the fact that the antenna is 65.0 cm long, and the value of Emax that you found.

 

[cmerickson21]

what equation would I use those in?

 

[Redbelly98]

Here's a hint: the units on Emax are V/m ... which could also be converted to V/cm if you like. You have the length in cm, as well as the number of Volts per cm ... so how many Volts?