(a) A thin plastic rod of length L carries a uniform linear charge density, λ-20 trCm,...
A plastic rod with uniform linear charge density λ is bent into the quarter circlea) Set up, but do not evaluate them here, definite integrals for the x-and y-components of the electric field at the origin in terms of λ, R, and ε0 or K . Clearly indicate your dq, r, dEx, and dEy on on the figureb) Evaluate the integrals and find the magnitude of the net electric field at the origin.
8 A semi-infinite thin rod has a uniform linear positive charge density λ and is located along the x-axis between x = x° (>0) and x = +ㆀ. Find the electric field at the origin. Hint: Ja .2 = a-b A.의 dx 1 B. 一巡i E. zero 8 A semi-infinite thin rod has a uniform linear positive charge density λ and is located along the x-axis between x = x° (>0) and x = +ㆀ. Find the electric field at...
A thin rod with uniform linear charge density... 3. A thin rod with uniform linear charge density of +9 mC/m lies in the xy plane vertically from the point (5,3) to the point (5,7) as shown. Point P is the point (8.2) Find the electric field at point P. Draw and label dq and r on the picture.
Week 3: Electric Field of Continuous Charge Distribution HW A plastic rod, shown on the right, has a uniform linear charge density λ and is bent into a quarter circle. Your goal is to find the electric field at the origin. 1 Label an arbitrary small piece of charge dq at an angle θ as shown in the figure. Draw a vector representing the field at the origin from that small piece of charge.2 Write expressions for the x- and y- components...
A long thin rod of length 2.0 m has a linear density λ(x) = Ax where x is the distance from the left end of the rod and A=3.0 kg/m. What is the mass (in kg) of the rod ?
Question 8 2 pts Consider a thin charged rod of length L, and uniform charge density (see figure). Find the electric field at this point. L Linear charge density 2 Suppose we wish to calculate the electric field at the dot indicated above, at (x,y)-coordinates given by (0, a). I.e., the dot is located on the y-axis, a distance a away from the rod (x-axis). Note: The rod is not centred on y-axis. Which expression will give the correct vertical...
A thin, uniform rod has length L and the linear density a (i.e. total mass M=al). A point mass m is placed at distance x from one end of the rod, along the axis of the rod. Calculate the gravitational force of the rod on the point mass m. (Hint: element of the mass is dM = adx) -GmM/x? O-GmM/(L2-x2) -GmM/(x+.5L) -GmM/(x2+Lx)
1. A thin rod of length L and total mass M has a linear mass density that varies with position as λ(x)-γ?, where x = 0 is located at the left end of the rod and γ has dimensions M/L3. ĮNote: requires calculus] (a) Find γ in terms of the total mass M and the length L. (b) Calculate the moment of inertia of this rod about an axis through its left end, oriented perpen dicular to the rod; expressed...
The charge per unit length on the thin rod of length L shown below is λ what is the electric field at the point P, distance a away from the right end of the rod? 1. Define a segment of charge: 2. Express the charge of one segment: 3. Express the E field of that one segment. 4. Integral each of the components of that field:
where λ is the charge density per unit length on the rod and εο is called the permittivity of free space (it is a universal constant with the value 8.854 x 10-12 F/m (farads per metre)) The integral for the electric field can be evaluated exactly using a method called trigonometric substitution with the result AL We won't learn the method of trigonometric substitution in this course; however, you will approximate the value of the integral using methods we introduced...