Question

Q5.An aircraft sometimes acquires small static charges. Suppose such an aircraft has 500 C charge and flies due west at a speed of 66 x10 cm/s over Earth's south magnetic pole with 80 HT magnetic field points straight down into the ground. Based on calculation, is the magnitude of the magnetic force on the plane negligible? How would be the magnitude of magnetic force change if the aircraft is flying in the same direction of magnetic field? Compare the angles between magnetic field and velocity, if the force experienced by moving this charged aircraft in a magnetic field, has maximum and minimum magnitude? If the charged aircraft is at rest, does magnetic field exert a force? Interpret your result. (6.0 Marks)

Answer 1

Here we have given that,

Charge q = 500 uC

Velocity v = 66 × 10^3 cm/s = 660m/s

Magnetic field B = 80 uT

Magnetic force over the aircraft will be as,

F = qvB sin(theta) .........1

Here theta is 90°

So that F = qvB = 2.64 × 10^-8 N

Which is quite negligible .

Now when the aircraft is flying in the same direction of the magnetic field then,

Angle between velocity and the magnetic field will be zero so that

Sin0 = 0

Hence F = qvB × 0 = 0

Which means now no magnetic force will be experienced by aircraft.

So there when aircraft is moving in the same direction of the magnetic field then

Angle between velocity and magnetic field is 0°

So in this case force will be 0

And when the velocity will make 90° with the magnetic field then this will make the force maximum over the aircraft.

Now in the next case ,

as we know here that the charges are moving only due to the magnetic field so if they are at rest means there would not be any magnetic field hence no velocity of the charge hence zero or no force will be there over the aircraft.

Means here v= 0

So F = 0

But if there is any magnetic field then charges automatically comes into velocity and force experienced by the aircraft .