A unit vector is basically a vector of magnitude 1 that says "go this way pl0x - I won't get in your way". Remember a force on a grid that was written like 5i-hat + 6j-hat? That says: "Please, go 5 units in the direction indicated by i-hat, then go 6 units in the direction indicated by j-hat! By...
Yes, k is constant.
To find a unit vector in some direction, divide the vector by its magnitude. For example, take a vector directed along the x-axis <5,0>. Dividing by the magnitude gives you <1,0>, the unit vector directed along the x-axis.
Your units for k are correct.
In this...
1. Yes, as evidenced by "When the conductor occupies this space, the induced field inside must exactly cancel this."
2. Yes, as evidenced by the equation (fixed) that I found for the electric field between two plates.
3. No. You have not described the orientation of the plate you are thinking...
From your description earlier, it looks like you're trying to this: draw the force line, then draw the tension lines from it to form a triangle. Is that right? If so, you will not get a correct answer out of this.
Something you could do with this triangle method is to draw both 10N lines...
I will show my steps and perhaps I can make my questions more clear. I understand they are quite vague right now. My apologies.
First, the space that is going to be occupied by the conductor has an electric field E = \frac{\sigma_0-\sigma_1}{2\epsilon_0}. When the conductor occupies this space...
Everything seems to be in order. Here's how to prove it:
Consider the force triangle formed by T_y and T. The angle opposite T_y is 30 degrees. The angle formed by T_y and T_x is 90 degrees. The angle formed by T and T_y must be 180-30-90=60 degrees. This force triangle is otherwise known as...
Thank you for the help. I figured out the answer after revisiting the problem a couple hours later. My mistake was taking the integral to find the charge of the semi-finite line before taking the integral for the electric field and thus the force. I simply needed to leave the integral as it was...
I know these must be true, and I've tried to solve the problem myself with these ideas in mind. Could you explain further why these ideas dictate that the induced field outside is 0, and the induced field inside is the negative charge distribution / electric constant? I understand why the two...
Homework Statement
An uncharged conducting slab is placed between two infinitesimally thin insulating plates with surface charge densities \sigma_1 and \sigma_2, respectively. Describe what fields are induced in the conducting slab and their magnitudes.
Homework Equations
None?
The...
I don't know how your teacher wants you to do it using pictures. I would probably draw a downward arrow that's 20cm long, then draw two up arrows that are both 10cm long somewhere else (labeling them as the T_y's), then use a protractor to measure an angle of 30 degrees and form the hypotenuse...
Might I chime in with a quick question about this problem? The normal force obviously provides an equal and opposite force to the forces pointing down perpendicular to the slide (whatever those may be, natty210). This would create a net force of 0 (equivalent to a pencil resting on a desk)...