An airplane is flying through a thundercloud at a height of 2100 m. (A very dangerous thing to do because of updrafts, turbulence,and the possibility of electric discharge.)
If there is a charge concentration of 20.7 C at height 3280 m within the cloud and −53.1 C at height 450 m, what is the magnitude of the electric field E at the aircraft? The Coulomb constant is 8.98755 × 10^9 N � m^2/C^2.
Answer in units of V/m
So I know F=kQq/r^2
E=F/q=kQ/r^2
I am assuming I have to find two electric fields...
I have tried this problem on my own multiple times and failed. Please help.
To find the magnitude of the electric field E at the aircraft, you need to calculate the electric field due to each individual charge concentration at their respective positions and then add them up. Here's how you can approach this problem step by step:
1. Calculate the electric field due to the charge concentration at 3280 m:
- Denote the charge concentration at 3280 m as Q1 = 20.7 C.
- The height of the aircraft is 2100 m, so the distance between the aircraft and the charge concentration is r1 = 3280 m - 2100 m = 1180 m.
- Plug these values into the formula for electric field: E1 = (k * Q1) / r1^2.
2. Calculate the electric field due to the charge concentration at 450 m:
- Denote the charge concentration at 450 m as Q2 = -53.1 C. Note that the negative sign represents the opposite charge.
- The height of the aircraft is 2100 m, so the distance between the aircraft and the charge concentration is r2 = 2100 m - 450 m = 1650 m.
- Plug these values into the formula for electric field: E2 = (k * Q2) / r2^2.
3. Add up the electric fields:
- Since electric fields are vector quantities, you need to consider their directions as well. In this case, the field due to Q1 will be in the opposite direction compared to the field due to Q2.
- Since the directions are opposite, you need to subtract E2 from E1 to get the net electric field E at the aircraft. Use the equation: E = E1 - E2.
4. Calculate the net electric field E:
- Plug in the values you calculated in steps 1 and 2 into the equation from step 3 to find the net electric field E at the aircraft.
5. Express the answer in units of V/m by using the fact that 1 N/C (newton per coulomb) equals 1 V/m (volt per meter).
Make sure to carry out the calculations carefully, keeping track of the units and signs of charges.