Square loop of copper wire- ks = side length ххх х х х X x x xBx Above this line: B uniform and horizontal s = side length Below this line: B = 0 d = wire diameter Urerminal

Two coplanar and concentric circular loops of wire carry currents of I, = 5.90 A and I, = 2.30 A in opposite directions as in the figure below. Let r, = 12.0 cm and r, = 8.60 cm. (Assume the positive direction along the axis perpendicular to the faces of the loops is out of the screen (towards you) and assume the positive vertical direction is toward the top of the screen.) (a) What is the magnitude of the net magnetic field (in µT) at the center of the two loops? PT (b) What is the direction of the net magnetic field at the center of the two loops? out of the screen O into the screen O toward the top of the screen O toward the bottom of the screen (c) Let r, remain fixed at 12.0 cm and let r, be a variable. Determine the value ofr, (in cm) such that the net field at the center of the loops is zero. cm

. The following picture shows a LONG conductor carrying current 1. Nearby there is a conducting rectangular loop with sides a = 8 cm and b = 4 cm. The loop also carries a resistance R = 10 ohms. The curent is constant and has a value of I = 6.0 Amperes. The loop is moving away to the right with a constant velocity, V = 2 m/s. Answer the following questions at the instant of time t" when the left edge of the loop is at position "x" as shown below Use the coordinate system , x to the right, y into the board, z upward a) Write an expression for the magnetic field as a function of the distance "x" (from the LONG conductor to the loop. ) USE “+" for CCW circulation and “.“ for CW circulation. b) Write the magnetic field in "i-j-k" format at point "x" to the right of the current carrying wire in the "i-zZ" plane R a c) Write the infinitesimal area vector for the loop in "i-j-k" format d) Write the explicit integral for the magnetic flux through the area of the loop using the answer for B and…

The figure shows two closed paths wrapped around two conducting loops carrying currents i₁ = 6.9 A and i₂ = 4.1 A. What is the value of the integral B ds for (a) path 1 and (b) path 2? (a) Number i (b) Number i Units Units