Can You Get Electrocuted On A Flight?

Oh the classic Brilliant E&M question...

First off, convert the velocity from km/h to m/s

$900 \frac{km}{h} = 250 \frac{m}{s}$

Now, as the conducting plane flies through this uniform magnetic field, the charges inside will feel a magnetic force which will cause the positive charges to move to the left tip. This new movement of charge (which is otherwise known as current) will also feel a magnetic force that will point backwards. So that means that the plane must be exerting a force so that it can maintain a constant velocity, thereby holding the force felt by the charges due to their initial northward velocity constant. This force is simply the electric force.

$F_{electric} = F_{magnetic}$

$Eq = q |v \times B|$

$E = vB$ (the velocity and magnetic field are always perpendicular)

Voltage in an ideal circuit is equal to the constant electric field within the circuit times the distance/length of the wire.

$V = Ed = vBd$

Plug in $250 \frac{m}{s}$ for $v$ , $50 \mu T$ for $B$ , and $60 m$ for $d$ .

$V = \boxed{0.75 V}$

B = 50 * 10^-6 T

v = 900 * 5/18 = 250 m/s

L = 60 m

emf = BLV

emf = 50 * 10^-6 * 250 * 60 = 0.75 volts

Use the concept of Motional EMF. The induced voltage is BvL = 0.75V, when numbers are plugged in with correct SI Units.

The voltage $V$ generated on moving a conductor by a magnetic field $B$ is given by Faraday's Law or the rate of change of magnetic flux: $V=\frac{\Delta (BA)}{\Delta t}$ , where $A$ is the area perpendicular to the magnetic field covered by the conductor in time $t$ .

For a plane flying with a speed $v = 900km/h$ , wingspan $l = 60m$ , in a constant magnetic field $B$ , the voltage generated:

$V=\frac{\Delta (BA)}{\Delta t} \Rightarrow V=\frac{B\Delta A}{\Delta t} = Bvl = 50 \times 10^{-6}\times \cfrac{900\times 1000}{60\times 60}\times 60 = \boxed{0.75}\space V$

Voltage/Potential difference = Work Done/ Time

Work Done = Force * Distance

Force = BQv

v = 250m/s

B= 50*10E-6

therefore, volt = 50*10E-6 * 250 * 60 = 0.75 V

E = Blv; B= 50 micro tesla; l=60m; v=900 km/hr=250 m/s; E= 0.75 V

EMF or electromagnetic force is the product of L, v and B where L is length in meters, v is the speed in m/s and B is in Tesla.