Above the xy plane (z > 0), there exists a magnetic material with µr1 = 2.0 and a field h~ 1 = 3.0 ˆx + 4.0 ˆz a/m. below the plane (z < 0) is free space. (a) find h~ 2 , assuming the boundary is free of surface current. what angle does h~ 2 make with a normal to the surface? (b) find h~ 2 , assuming the boundary has a surface current k~ = 3.0 ˆx a/m.

Agardener uses a wheelbarrow to move soil from a truck to his garden. on the first trip from the truck to the garden, the wheelbarrow is half-full of soil and the gardener applies a certain force to cause it to accelerate. on the second trip, the wheelbarrow is full of soil. although the gardener applies the same amount of force to the wheelbarrow, he cannot move it with the same rate of acceleration. what should the gardener do to move the wheelbarrow at the same rate of acceleration for the second trip?

Part f - example: finding two forces (part i) two dimensional dynamics often involves solving for two unknown quantities in two separate equations describing the total force. the block in (figure 1) has a mass m=10kg and is being pulled by a force f on a table with coefficient of static friction îľs=0.3. four forces act on it: the applied force f (directed î¸=30â above the horizontal). the force of gravity fg=mg (directly down, where g=9.8m/s2). the normal force n (directly up). the force of static friction fs (directly left, opposing any potential motion). if we want to find the size of the force necessary to just barely overcome static friction (in which case fs=îľsn), we use the condition that the sum of the forces in both directions must be 0. using some basic trigonometry, we can write this condition out for the forces in both the horizontal and vertical directions, respectively, as: fcosî¸â’îľsn=0 fsinî¸+nâ’mg=0 in order to find the magnitude of force f, we have to solve a system of two equations with both f and the normal force n unknown. use the methods we have learned to find an expression for f in terms of m, g, î¸, and îľs (no n).

Uppose we consider the system of the three capacitors as a single "equivalent" capacitor. given the charges of the three individual capacitors calculated in the previous part, find the total charge qtot for this equivalent capacitor. express your answer in terms of v and c.