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.
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 of the electric field at the origin due to your chosen small piece of charge.
3 Write, but do not evaluate, definite integrals for the x- and y- components of the net electric field at the origin.
4 Evaluate the integrals and write the net electric field in component form.
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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.
A plastic rod with uniform linear charge density λ is bent intothe quarter circlea)...
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.
2. Calculate the electric field of a thin rod of uniform charge density λ is bent...
2. Calculate the electric field of a thin rod of uniform charge density λ is bent into the shape of an arc or radius R. The arc subtends a total angle of 28, symmetric about the x-axis as shown in the figure. What is the electric field at the origin O. Give the answer in terms of the variables in the question.
Problem 1 A curved plastic rod of charge +Q forms a semi-circle of radius R in...
Problem 1 A curved plastic rod of charge +Q forms a semi-circle of radius R in the x-y plane, as shown below on the left. The charge is distributed uniformly across the rod. dQ +0 +Q Now let's analytically determine the magnitude and direction of the electric field E at the center of the circle using polar coordinates and the charge element dQ shown in the image on the right. write down an expression for the electric field dE at...
Q1. A curved plastic rod of charge+Q forms a semi-circle of radius R in the x-y...
Q1. A curved plastic rod of charge+Q forms a semi-circle of radius R in the x-y plane, as shown below on the left. The charge is distributed uniformly across the rod. dQ +Q +Q Now let's analytically determine the magnitude and direction of the electric field E at the center of the circle using polar coordinates and the charge element dQ shown in the image on the right Write down an expression for the electric field dE at the center...
A rod of length H has uniform charge per length λ. We want to find the...
A rod of length H has uniform charge per length λ. We want to find the electric field at point P which is a distance L above and distance R to the right of the rod. Use the diagram below for the next three questions. What is the charge dq in the small length du of the rod? du: +x Call the integration variable u with u-0 chosen to be at point A and +u defined as down. What is...
(a) A thin plastic rod of length L carries a uniform linear charge density, λ-20 trCm,...
(a) A thin plastic rod of length L carries a uniform linear charge density, λ-20 trCm, along the x-axis, with its left edge at the coordinates (-3,0) and its right edge at (5, 0) m. All distances are measured in meters. Use integral methods to find the x-and y-components of the electric field vector due to the uniformly-charged charged rod at the point, P. with coordinates (0, -4) m. 4, (o, 4 p2212sp2018 tl.doex
A thin plastic rod bent into a semicircular arc find electric field and momentum
consider a thin plastic rod bent into a semicircular arc of radius R with center at the origin. The rod carries a uniformly distributed negative charge -Q.(a) Determine the electric field \(\vec{E}\) at the origin contributed by the rod. (Indicate the direction with the sign of your answer. Use any variable or symbol stated above along with the following as necessary: \(\left.\varepsilon_{0} .\right)\)\(E_{x}=\)\(E_{y}=\)(b) An ion with charge \(-4 e\) and mass \(M\) is placed at rest at the origin. After...
10. Find the electric field at the origin for a line of charge density λ on...
10. Find the electric field at the origin for a line of charge density λ on the y 0 portion of the unit circle in the r-y plane if (a) λ is constant (b) λ= cos φ z sin
A wire having a uniform linear charge density λ is bent into the shape shown in the figure below. Find the electric potential at point O.
A wire having a uniform linear charge density λ is bent into the shape shown in the figure below. Find the electric potential at point O.
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?
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:
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.
2. Calculate the electric field of a thin rod of uniform charge density λ is bent into the shape of an arc or radius R. The arc subtends a total angle of 28, symmetric about the x-axis as shown in the figure. What is the electric field at the origin O. Give the answer in terms of the variables in the question.
Problem 1 A curved plastic rod of charge +Q forms a semi-circle of radius R in the x-y plane, as shown below on the left. The charge is distributed uniformly across the rod. dQ +0 +Q Now let's analytically determine the magnitude and direction of the electric field E at the center of the circle using polar coordinates and the charge element dQ shown in the image on the right. write down an expression for the electric field dE at...
Q1. A curved plastic rod of charge+Q forms a semi-circle of radius R in the x-y plane, as shown below on the left. The charge is distributed uniformly across the rod. dQ +Q +Q Now let's analytically determine the magnitude and direction of the electric field E at the center of the circle using polar coordinates and the charge element dQ shown in the image on the right Write down an expression for the electric field dE at the center...
A rod of length H has uniform charge per length λ. We want to find the electric field at point P which is a distance L above and distance R to the right of the rod. Use the diagram below for the next three questions. What is the charge dq in the small length du of the rod? du: +x Call the integration variable u with u-0 chosen to be at point A and +u defined as down. What is...
(a) A thin plastic rod of length L carries a uniform linear charge density, λ-20 trCm, along the x-axis, with its left edge at the coordinates (-3,0) and its right edge at (5, 0) m. All distances are measured in meters. Use integral methods to find the x-and y-components of the electric field vector due to the uniformly-charged charged rod at the point, P. with coordinates (0, -4) m. 4, (o, 4 p2212sp2018 tl.doex
10. Find the electric field at the origin for a line of charge density λ on the y 0 portion of the unit circle in the r-y plane if (a) λ is constant (b) λ= cos φ z sin
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