Question

A 180 g model airplane charged to 18 mC and traveling at 2.2 m/s passes within 8.6 cm of a wire, nearly parallel to its path, carrying a 30 A current. What acceleration (in g's) does this interaction give the airplane?

Answer 1

`a=0.2*10^(-5)g`

Step-by-step explanation:

From the question we are told that:

Mass
`M=180=>0.18kg`

Charge
`Q=18mC=18*10^-^3C`

Velocity
`v=2.2m/s`

Length of Wire
`L=8.6cm=>0.086`

Current
`I=30A`

Generally the equation for Magnetic Field of Wire B is mathematically given by

`B=(\mu_0*I)/(2\pi*l)`

`B=(4*3.14*10^-^7*I)/(2*3.14*8.6)`

`B=6.978*10^(-5)T`

Generally the equation for Force on the plane F is mathematically given by

`F=qvB`

Therefore

`ma=qvB`

`a=(qvB)/(m)`

`a=(18*10^(-5)83.4*6.978*10^(-5))/(0.18kg)`

`a=2.37*10^(-5)`

Therefore in Terms of g's

`a=(2.37*10^(-5))/(9.8)`

`a=0.2*10^(-5)g`