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prohojiy [21]
3 years ago
12

Find an expression for the electric field e⃗ at the center of the semicircle. hint: a small piece of arc length δs spans a small

angle δθ=δs /r, where r is the radius.
Physics
1 answer:
ahrayia [7]3 years ago
8 0
Let l = Q/L = linear charge density. The semi-circle has a length L which is half the circumference of the circle. So w can relate the radius of the circle to L by 

<span>C = 2L = 2*pi*R ---> R = L/pi </span>

<span>Now define the center of the semi-circle as the origin of coordinates and define a as the angle between R and the x-axis. </span>

<span>we can define a small charge dq as </span>

<span>dq = l*ds = l*R*da </span>

<span>So the electric field can be written as: </span>

<span>dE =kdq*(cos(a)/R^2 I_hat + sin(a)/R^2 j_hat) </span>

<span>dE = k*I*R*da*(cos(a)/R^2 I_hat + sin(a)/R^2 j_hat) </span>

<span>E = k*I*(sin(a)/R I_hat - cos(a)/R^2 j_hat) </span>

<span>E = pi*k*Q/L(sin(a)/L I_hat - cos(a)/L j_hat)</span>
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