Small spiders are known to fly from place to place by letting out a length of silk, which then carries them around. Recently it was discovered that they're actually using the electric field of the Earth to do this. Let us explore what a spider experiences.

Let us first model the flying spider as a charged object with charge $Q,$ mass $M($ignore the silk for now$).$ It experiences gravity from the Earth as well as a downward pointing electric field. The spider is hovering motionless above the ground.

a$.$ Do you expect the sign of the charge to be positive or negative?

b$.$ Draw the free body diagram of the charged spider

c$.$ If the mass and electric field are known, what is the charge that is needed to float the spider motionless?

d$.$ If instead of motionless, the spider is accelerating upwards with an acceleration a$,$ compute the charge.

$2.$

The spider from the last problem is now in the electric field of the wall from the example problem. It now experiences an electric field from the Earth in the $-y$ direction with a value of Ey and one in the $-x$ direction with a value of Ex$.$

a$.$ Draw the free body diagram of the spider

b$.$ Find an expression for the magnitude and direction of the resultant electric field.

c$.$ Find an expression for the magnitude and direction of the total force on the spider.

Small spiders are known to fly from place to place by letting out a length of silk, which then carries them around. Recently it was discovered that they're actually using the electric field of the Earth to do this. Let us explore what a spider experiences.

Let us first model the flying spider as a charged object with charge $Q,$ mass $M($ignore the silk for now$).$ It experiences gravity from the Earth as well as a downward pointing electric field. The spider is hovering motionless above the ground.

a$.$ Do you expect the sign of the charge to be positive or negative?

b$.$ Draw the free body diagram of the charged spider

c$.$ If the mass and electric field are known, what is the charge that is needed to float the spider motionless?

d$.$ If instead of motionless, the spider is accelerating upwards with an acceleration a$,$ compute the charge.