The strength of the earth’s magnetic field b at the equator is approximately equal to 5 × 10−5 t. the force on a charge q moving in a direction perpendicular to a magnetic field is given by f = q v b, where v is the speed of the particle. the direction of the force is given by the right-hand rule. suppose you rub a balloon in your hair and your head acquires a static charge of 9 × 10−9 c. if you are at the equator and driving west at a speed of 90 m/s, what is the strength of the magnetic force on your head due to the earth’s magnetic field? answer in units of n. what is the direction of that magnetic force?

1. Magnitude:

The magnitude of the magnetic force exerted on your head by the Earth's magnetic field is:

where we have:

is the charge on the head

v = 90 m/s is the magnitude of the velocity

is the strength of the magnetic field

is the angle between the direction of B and v (they are perpendicular)

Substituting into the equation, we find

2. Direction: upward

The direction of the magnetic force can be found by using the right hand rule. We have:

- index finger: direction of velocity --> west

- middle finger: direction of magnetic field --> south (the magnetic field of the Earth goes from north pole to south pole)

- thumb: direction of the force --> upward

So, the direction of the magnetic force is upward.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

it is given that trillions of microbes make up to 1% to 3% of the body mass.

let's take average of this percentage: 2%

consider the average mass of the human body as 70 kg.

then, trillions of microbes would have mass  

therefore, 100 trillion micro-organisms would weigh:

this is an approximate value and could change depending on the mass of the human body and percentage of the microbes present in it.

average mass per microorganism =