An aeroplane in flying horizontally from w to e with velocity of 900km...
**Calculation of Force on the Airplane**
To calculate the force on the airplane due to the Earth's magnetic field, we need to consider the formula for magnetic force:
F = q * v * B * sin(theta)
Where:
F is the magnetic force
q is the charge of the particle
v is the velocity of the particle
B is the magnetic field strength
theta is the angle between the velocity and the magnetic field vectors
In this case, the charge of the airplane is not given, but we can assume it to be neutral (q = 0). Therefore, the force on the airplane due to the Earth's magnetic field can be simplified to:
F = 0 * 900 km/hr * 5x10^-4 T * sin(30 degrees)
Since the charge is zero, the force will also be zero. This means that the Earth's magnetic field does not exert any force on the airplane.
**Explanation**
1. Magnetic Force Formula:
The formula for magnetic force on a charged particle moving through a magnetic field is given by F = q * v * B * sin(theta), where q is the charge of the particle, v is its velocity, B is the magnetic field strength, and theta is the angle between the velocity and the magnetic field vectors.
2. Charge of the Airplane:
The charge of the airplane is not given in the question. However, since airplanes are made of mostly neutral materials, we can assume that the charge of the airplane is zero (q = 0).
3. Velocity of the Airplane:
The velocity of the airplane is given in the question as 900 km/hr. However, it is important to convert this velocity to SI units before using it in the formula. 900 km/hr is equivalent to 250 m/s.
4. Magnetic Field Strength:
The question states that the horizontal component of the Earth's magnetic field is 5x10^-4 T.
5. Angle of Deflection:
The question also states that the angle of deflection is 30 degrees. This is the angle between the velocity of the airplane and the magnetic field.
6. Calculation:
Using the formula for magnetic force, we substitute the given values into the equation:
F = 0 * 250 m/s * 5x10^-4 T * sin(30 degrees)
= 0
This calculation shows that the force on the airplane due to the Earth's magnetic field is zero. Therefore, the Earth's magnetic field does not exert any force on the airplane.