Homework 1-4 Find all the force vectors and then add the vectors to find the total force

What is the Electric field a distance r away from an infinite line of charge? a x L What direction is the E-field? dq

Estimate the Volume and Surface area of a Basketball. ●using the formulas for a sphere, namely V = 4/3PI*r^3 and SA = 4PI*r^2 and estimating the radius to be 5 inches, the volume would be about cubic inches and the surface area would be about 314 square inches. ●Well, I estimate that the diameter of a basketball is around 9 inches, giving a radius of 4.5 inches. (ok, I admit, I did a quick search on Google.) Volume is 4/3 pi r^3 which comes to 382 in^3. Surface area is 4 pi r^2 which comes to 254 in^2. If by some chance I forgot the formulas for volume and surface area, I could also do it by integration. ●I know that both the surface area and the volume will be less than a full meter each, and I can estimate the diameter of a basketball to be about 30 cm, making the radius 15cm. The volume and surface area would be.014 meters cubed, and.283 meters squared. ●VOLUME SURFACE AREA eqn: (4/3)*pi*r^3 eqn: 4pi*r^2 rad: 9in = 22.86cm rad: 9in = 22.86cm volume: cm^3 surface area: cm^2

In the packet –What does it mean to integrate?

How do I find the surface area?

How to find the volume of a sphere. Imagine the sphere is made up of thin spherical shells of radius r and thickness dr. The volume of each spherical shell is given by the surface area of the spherical shell multiplied by the thickness of the shell.

Imagine that you have been asked to calculate, using integration, the volume of a Football. Please describe briefly how you would set up this calculation. Pay particular attention to how you would "slice" the object or in other words what would be your variable of integration and why? ●I would slice it up so that the slices are perpendicular to the oblong direction (so that the cross section of the slices are a circle). I would do this so that the variable of integration could be the radius. ●if the football is laying on its side, you add up all areas of the circles from end to end. the radius is what is changing, so r is the variable of integration. ●I would integrate the football using slices with a thickness of dz. This means that each slice would be parallel with the xy plane. Each slice would be a circle so we could use the area of a circle to find the total volume. I would need some sort of an equation to find a relationship between the radius of each slice and the z axis. If given all this information, I could then find the volume of the football. ●volume = circumference times height times thickness we positioned the football upright along y- axis and sliced them into cylinders with circular cross section facing facing up.

Approximate a football by revolving the curve y=1-z 2, -1≤z≤1 about the z-axis. What is its volume?

Now find the mass If it is a nerf then the density is constant

Now assume the density increases proportional to the inverse of the radius. Find the mass.

How do I know how to slice it? If everything is uniform it does not matter. If density depends on z usually use dz. If density depends on r usually use dr. If you can easily calculate one area, use it. Choose the simplest integral to do. If it becomes complicated maybe there is a better way.

How much water is in the cup if tipped so water just touches one lip and a diameter of the bottom? What do I want to use as my variable of integration? How do I slice it? x y z

What is its volume?

What is the volume enclosed by the x, y, z and the plane shown? How do I slice it?

The hemisphere shown is charged uniformly with a positive surface charge density. At the origin, what direction is the electric field? A. +x direction B. +y direction C. +z direction D. Something else not along a x,y, or z axis E. Zero magnitude – thus no direction

Now find the Electric Field BE Careful, r is the distance from dq to the point you are looking at (not usually the same r as in dq)