A horizontal antenna of length L =100 m, which is distance h = λ/2 from the ground, carries
current I(t) = I0 sin(ωt), where I0 = 10A and ω = 2π105

rad/s. A) Check if it is short or long
antenna and write down the corresponding solutions for electric E~ and magnetic H~ fields large
distance r from the antenna (choose coordinate axes so that Z axis is along the antenna and the
X axis is vertical); B) Calculate the amplitude of the magnetic field r = 10 km away from the
antenna in the ZX plane at the polar angle of θ = π/6 with respect to the Z-axis above the ground;
C) Sketch the radiation patterns in the ZX and XY planes.

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.