Find the distance
x on the axis perpendicular to the center of a ring of radius
R = 0.1 m and total charge
Q = 1e-6 C such that a point charge
q = 1e-9 C located at
x experiences a force of
F_target = 5.1 N.
program ring_force_bisection implicit none real :: k, Q, q, R, F_target real :: a, b, c, x, Fx, Fa, Fb ! Coulomb constant k = 9e9 ! Total charge on ring (in C) Q = 1e-6 ! Point charge (in C) q = 1e-9 ! Radius of ring (in m) R = 0.1 ! Target force (in N) F_target = 5.1 ! Initial guesses for x a = 0.01 b = 0.2 ! Evaluate F(a) and F(b) Fa = k*Q*q*a / ((a**2) + (R**2))**1.5 Fb = k*Q*q*b / ((b**2) + (R**2))**1.5 ! Bisection method do while (b - a > 1e-6) ! Compute midpoint c = (a + b) / 2 ! Evaluate F(c) Fx = k*Q*q*c / ((c**2) + (R**2))**1.5 ! Check sign of F(c) and update a or b if (Fx*Fa > 0) then a = c Fa = Fx else b = c Fb = Fx endif end do ! Compute final value of x x = (a + b) / 2 ! Print result write(_,_) "The distance x where the force is 5.1 N is:", x, "m" contains ! Add any additional functions or subroutines here, if needed. end program ring_force_bisection