Ask Question
21 January, 17:49

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.

+5
Answers (1)
  1. 21 January, 20:12
    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

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

    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.

    we can define a small charge dq as

    dq = l*ds = l*R*da

    So the electric field can be written as:

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

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

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

    E = pi*k*Q/L (sin (a) / L I_hat - cos (a) / L j_hat)
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “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 ...” in 📙 Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers