Suppose that we can use wire of 1.0-mm diameter to make either a single loop of wire or a solenoid, and we wish to compare, for a given current, the magnetic fields at the center of each.

a. Use the Biot-Savart law to derive an expression for the magnetic field magnitude at the center of a circular current loop. Express your answer in terms of the current I, loop radius R, and magnetic constant muknot.
b. Compare the magnitude of the magnetic field at the center of a circular loop of radius 40 mm with the magnitude of the magnetic field at the center of a solenoid of the same radius and with 3.0 turn per millimeter. Assume the current is the same through the current loop and the solenoid.

Determine the amount of work done when a crane lifts a 100-n block form 2m above the ground to 6m above the ground

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.

Where do magnetic lines of force enter earth?