Equilateral triangle Definition and 105 Threads

2 particles of charge q are placed at 2 vertices of an equilateral triangle of side a. An electric dipole is placed at the third vertex with its dipole moment orientated parallel to the opposite side of the triangle. a) Determine the magnitude of the torque on the dipole due to the electric...

Homework Statement Lets say I have an equilateral triangle, and you are asked to calculate the net force on the top of the triangle Homework Equations Coulombs Law The Attempt at a Solution I know to use Coulombs law to find the forces acting on the top of the triangle, then since...

A line divides an equilateral triangle into two parts with the same perimeter and having areas $A_1$ and $A_2$ respectively. Prove that $\dfrac{7}{9} \le \dfrac{A_1}{A_2} \le \dfrac{9}{7}$.

Homework Statement Three rods each of uniform charge Q and length a are formed into an equilateral triangle. Given[Q,a,q] determine: 1. The voltage at the center of the triangle. 2. If a charge -q is placed at the center of the triangle determine potential energy. 3. Determine the initial...

Homework Statement I got an answer as you can see in both pictures, but apparently it is wrong. What did I do? Homework Equations The Attempt at a Solution In this picture I found the y components of the electric field at C. Since the bottom 2 are the same i just doubled one of...

Homework Statement Three point charges have equal magnitudes, two being positive and one negative. These charges are fixed to the corners of an equilateral triangle. The magnitude of each of the charges is 2.9 µC. The lengths of the sides of the triangle are .02m Calculate the magnitude...

P is an inner point of equilateral triangle ABC , given PC=3, PA=4,PB=5 ,please find the side length of the equilateral triangle

Homework Statement I'm trying to express the function of a equilateral triangle as a function of the length of a side. All you know is the sides are all equal Homework Equations I have the answer but i don't understand (how and why they got there) and they used the A of a triangle as A=...

Hi all, How would you determine the angle i in the following equilateral triangle. Thank you.

Homework Statement Question is attached. I know there's a few ways to solve this, but I'm wondering specifically why my integral of F ds isn't working. Homework Equations F = k * q^2 / r^2 U = ∫ F ds cos 30 = √3/2 s= rcos30 The Attempt at a Solution U = 2 * cos 30 * k *...

Homework Statement See attached image Homework Equations 1/4πε*q/r The Attempt at a Solution I know that since the problem gives centimeters, there are initial changes to units to be made in the permittivity constant. This makes it 8.86x10^-9 N/nanoCoulombs and 100 mm. But...

Homework Statement y=x^2 y=1 Find the volume of the bounded region using an equilateral triangle cross section Homework Equations c^2=a^2+b^2 The Attempt at a Solution I'm will solve it with respect to x 1st. 2∫((1-x^2)h)/2 dx from 0 to 1 base=2(1-x^2) (2-2x^2)^2=(1-x^2)^2+h^2 4-8 x^2+4...

Homework Statement Suppose T is an equilateral triangle on the sphere of radius R = 1. Let \alpha denote the angle at any of the three vertices’s of the triangle. (Recall that 3\alpha > n.) Use the result of the last problem on the previous homework and the inclusion - exclusion principle...

Homework Statement These are really frustrating because they seem so simple, I work them all out without a hitch only to find that I'm wrong half the time and left wondering why. In fig 21-26a, particles 1 and 2 have charge 20 microcoulombs each and are held at separation distance d = 1.5...

Homework Statement Hello, so I'm going to be a freshman physics major next year, and over the summer I'm trying to improve my problem solving skills. I've started going through Irodov's problems in general physics, and I have a question about two different solutions to one of the problems...

The problem is to find the moment of inertia for a solid equilateral triangle about an axis at the triangle's vertex which is perpendicular to the plane of the triangle. Mass is given as M. I was wanting to treat it like 3 point masses at each vertex with 1/3 mass. Then I could use the sum...

The base of a solid is the region bounded by the parabola x2 = 8y and the line y = 4 and each plane section perpendicular to the y-axis is an equilateral triangle. What is the volume of the solid?(Barron's Problem) so I solved for x since y must be used because the cross section is...

Homework Statement The distances from the vertices of an equilateral triangle to an interior point P are √a, √b, and √c respectively,where a, b, and c are positive integers. Find the minimum and the maximum values of the sum a + b + c if the side of a triangle is 13. Homework Equations the...

Homework Statement Charges Q, Q, and q lie on the corners of an equilateral triangle with sides of length a. Charge q lies on the top corner with Q and Q on the left and right corners. (a) What is the force on the charge q? (b) What must q be for E to be zero half-way up the altitudeat...

Homework Statement Three point charges are located at the corners of an equilateral triangle as in the figure below. calculate the net electric force on the 7-nc charge. Each sides are .5 m. (q1=7μc) (q2=2 μc) (q3= -4 μc) ___1 __/__\ 2/____\3 Homework...

Hey Guys, My question involves finding all of the forces acting upon each member. It is known that each side of the triangle has a length of l. It is also known that the force is acting at the very top of the triangle in the x direction (to the right) labelled as F. Attempt: I found moments...

Homework Statement A point charge q = +2.0 µC is placed at each corner of an equilateral triangle with sides 0.23 m in length. What is the magnitude of the electric field at the midpoint of any of the three sides of the triangle? 3. I want to know if I did this correctly, or totally...

Given an equilateral triangle ABC, P is any point inside it where PA = 3, PB = 4 and PC = 5. Find area of the triangle using the Law of Sines or Law of Cosines.

Homework Statement Based on my understanding of the question the diagram should be like this ABC is an equilateral triangle with side 2a.Two circle are are drawn , with one of them crossing the points A,B and C.another circle crossess B and C with A as centre Prove that the area enclosed by...

Homework Statement Three triangles are placed into a circle; The vertices of the triangle are tangential to each circle. How do you find the ratio of the area of the circles to that of the triangle? Homework Equations pi r^2, 1/2(b)(h), sqrt3/4 * a^2 (2r^2). The Attempt at a...

Homework Statement http://www.ridemtl.com Homework Equations F = k(q1q2/r^2)The Attempt at a Solution I know pretty much what to do for the problem, but I cannot get the right answer. I think my issue lies within what angles I am using for the components. Because it is an equilateral triangle...

[b]1. Homework Statement [ what is the distance from one corner of an equilateral triangle of sides a to the circumcentre? I can figure out the length from one corner to the opposite side to be sqrt3*a/2 but that's about it. I just can't see how to do this. thanks

Homework Statement [PLAIN]http://img59.imageshack.us/img59/9484/fp5.gif to find the moment of inertia through point A Homework Equations I = \int{r^2dm}The Attempt at a Solution Used a double integral from point A: \displaystyle\int_{0}^{h}\displaystyle\int_{-L/2}^{L/2}\rho(x^2+y^2)dxdy =...

Homework Statement An object moves around a equilateral triangle with a constant speed (magnitude of velocity is constant) of 22.3 m/s. If it moves from the starting to ending point (as shown below) in a time of 12.69 seconds, what is the magnitude of the average acceleration vector in m/s2...

Homework Statement Consider an equilateral triangle of side 15.6 cm. A charge of +2.0 µC is placed at one vertex and charges of –4.0 µC each are placed at the other two, as shown in the diagram to the right. Determine the electric field at the centre of the triangle. I've found the...

[Homework Statement 1.) Three charges are placed 25 cm apart in an equilateral triangle. Q1 has a charge of -6.0 nC, q2 has a charge of 4.0 nC and q3 has a charge of 4.0 nC. what is the force on q2? q1 is the top point, q2 is the bottom left leaving q3 on the bottom right Homework...

Homework Statement I had this exam question for a final exam and I was wondering if I got it right or not. There are three point charges +4q equally spaced apart at the tips of an equilateral triangle with distance .11m apart from each other. What is the magnitude of the electric field at the...

In an equilateral triangle a positive point charge +q is located at each of the vertices. If a 4th charge is added at the midpoint between one of the sides could this charge be such that the force on it would be zero?

Volume by cross-section: ellipse and equilateral triangle cross sections?? Homework Statement The base of a solid is the region bounded by the ellipse 4x^2+9y^2=36. Find the volume of the solid given that cross sections perpendicular to the x-axis are: a) equilateral triangles b) squares...

Homework Statement A particle moves from rest and has impressed a uniform velocity of 10 meters per second parallel to one side of an equilateral triangle, and a uniform acceleration of 10 meters/sec2 parallel to an adjacent side of the triangle. Find the distance of the particle from its...

Homework Statement 3 equal point charges on the vertices of a triangle. If the each of the charges are doubled, why is the resulting force on each charge quadrupled? Homework Equations F= Fx +Fy F= kqk2/r^2 The Attempt at a Solution I got doubled

Homework Statement What is the electric potential at point P, the center of an equilateral triangle with side length of 2a and total charge of Q? Use infinity as the reference point. Homework Equations ∆v = -∫E∙ds v(r)= kq/r The Attempt at a Solution I already have the...

Homework Statement The height h of an equilateral triangle is increasing at a rate of 3cm/min. How fast is the area changing when h is 5cm. Give to 2 decimal places. Homework Equations The Attempt at a Solution Im kind of stumped with this one because the question doesn't...

Homework Statement point p,charge Q1,Q2 are on the vertices of an equilateral triangle of side 1.0m.find the resultant force acting on a charge of +2c placed at P a)when Q1=-5c,Q2=+5c b)when Q1=-5c,Q2=-5c

How many symmetries (and what symmetries) and how many elements do the transformation groups of the equilateral triangle and the icosahedron have? thanks

Hello! In a book I was reading it spoke (if a book can speak) of Equilateral Triangles when used for comparing three variables (the one where the x=0, y=0 and z=0 refer to the left, right and bottom of the triangle respectively, then a point is plotted depending on what the point being plotted...

Three identical stars of mass M form an equilateral triangle that rotates around the triangle's center as the stars move in a common circle about that center. The triangle has edge length L. What is the speed of the stars? All I've been able to come up with is they rotate around the...

Homework Statement and why is it FLcos(30)? Homework Equations The Attempt at a Solution So by looking at the soln, D(distance)=Lcos(30), which should be the hieght of the traingle. But the distances between a the forces at any point don't always add up to the hieght.. I am confused

Three positive and equal charges Q1, Q2, and Q3 are at the corners of an equilateral triangle. Point P is at the midpoint of the line between Q1 and Q3 (the middle of the bottom of the equilateral triangle). The electric field at P is A.zero b. not zero and directed along the line from P to Q3...

Homework Statement Two long straight wires sit at the lower corners of an equilateral triangle and carry current I. Find the magnitude and direction of the B field at the top vertex of the triangle for the case where: a) the current in both lower wires flows out of the page b) the...

Homework Statement Show that the curve x^3+3xy+y^3=1 contains only one set of three distinct points A,B, and C, which are vertices of an equilateral triangle. Homework Equations The Attempt at a Solution I randomly starting plotting points and found that all of them fell on the line...

Homework Statement Three rigid rods are joined to form an equilateral triangle ABC of side 1m.Three particles carrying charge 1C are placed at the vertices.The whole system is in equilibrium in an inertial frame.What is the magnitude of the net force on each of the charges? Homework...

Homework Statement Determine the surface area and volume of a solid formed by rotating an equilateral triangle of side a about its base. Homework Equations The Attempt at a Solution ----------working out surface area-------- Integral of 2.pi.y dx with limits of a and 0. I...

Homework Statement Three 8 cm long rods form an equilateral triangle. Two of the rods are charged to +8 nC, the third to -8 nC. What is the electric field strength at the center of the triangle? Homework Equations E = 4piKλL The Attempt at a Solution I found the radius of the...

The three charges are held in place below. L = 1.40 m. (a) Find the electric potential at point P. (b) Suppose that a fourth charge, with a charge of 6.73 μC and a mass of 4.71 g, is released from rest at point P. What is the speed of the fourth charge when it has moved infinitely far away...