How Is Force Calculated on a Charge at the Center of a Charged Semicircle?

In summary, a homework problem asks to calculate the total force on a charge at the center of curvature of a semicircle with a radius of 60.0 cm and a charge per unit length described by [lamb]naught cos [the]. The total charge on the semicircle is 12.0 microcoulombs and the angle [the] is formed by dragging R clockwise from the positive y axis. The book's answer is -0.707Nj while the person asking for help got -0.526N. They are seeking assistance in figuring out the correct solution.
  • #1
mateoguapo327
help! I need help with this homework problem.

--A line of positive charge is formed into a semicircle of radius R=60.0 cm. The charge per unit length along the semicircle is described by the expression [lamb]= [lamb]naught cos [the] . The total charge on the semicircle is 12.0 microcoulombs. Calculate the total force on a charge 3.00 microcoulombs at the center of curvature.--

The figure shows the semicircle with is center at the origin going from 0 to pi. [the] is the angle formed by dragging R clockwise from the positive y axis.

the answer in the book is -0.707Nj and I got -0.526N. Can someone please help me figure out how to properly go about solving this problem?
 
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  • #2
I know you're new here and all...

but shouldn't this go in the homework help section? you might get a better response there.
 
  • #3


Sure, I can help you with this problem. First, let's break down the steps to solve it:

1. Find the expression for the charge per unit length, [lamb], along the semicircle:
Since we know that the total charge on the semicircle is 12.0 microcoulombs and the radius is 60.0 cm, we can use the formula for circumference (C = 2πr) to find the total length of the semicircle:
C = 2π(60.0 cm) = 120π cm
Since this length is for the entire circle, we need to divide it by 2 to get the length of the semicircle:
L = 120π cm / 2 = 60π cm
Now, we can use the given expression [lamb] = [lamb]naught cos [the] to find the charge per unit length:
12.0 microcoulombs = [lamb]naught * cos(pi/2)
Solving for [lamb]naught, we get:
[lamb]naught = 12.0 microcoulombs / cos(pi/2) = 12.0 microcoulombs / 0 = undefined
Since [lamb]naught is undefined, we can't use this expression to find the charge per unit length. However, we can still solve the problem using the given information.

2. Find the force on a charge of 3.00 microcoulombs at the center of curvature:
To find the force, we can use the formula for electric force:
F = k * [q1] * [q2] / r^2
Where k is the Coulomb's constant (9.0 x 10^9 Nm^2/C^2), [q1] is the charge on the semicircle, [q2] is the charge at the center of curvature, and r is the distance between them.
Since we are looking for the force at the center of curvature, r = 60.0 cm.
Substituting the given values, we get:
F = (9.0 x 10^9 Nm^2/C^2) * (12.0 microcoulombs) * (3.00 microcoulombs) / (60.0 cm)^2 = 9.0 x 10^9 *
 
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