Stuck on these 3 questions, help me please! Show work for each problem, thanks!
ID: 2106103 • Letter: S
Question
Stuck on these 3 questions, help me please! Show work for each problem, thanks!
A metal, u-shaped bar is situated so that its two ends are each resting in a cup of mercury. The bar is in a uniform magnetic field which is orthogonal to the bar. When a current is applied through the mercury and bar, it experiences a force that will send it flying upward, (a) Draw a sketch and label all relevant vectors involved in this scenario. If the bar has mass of 200g, a length of 15 cm, and the magnetic field has a magnitude of 0.2T, what must be the minimum current (direction and magnitude) to lift the bar? In a particular region, there is a uniform current density of 100 Aim2 in the positive z direction. What is the value of B ds when that line integral is taken along the three straight-line segments from (4d, 0, 0) to (4d, 3d, 0) to (0,0,0) to 4d, 0,0), where d is 2 cm? How long would it take, following the removal of the battery, for the potential difference across the resistor of an RL circuit to decay to 10% of its initial value? (Take L = 2.00H, R = 3.00 Ohm).Explanation / Answer
1) so the bar will feel a force down from gravity and a force up from the magnetic field
so to just barely moving
F mangetic= mg
I L B = m g
I = mg/(BL) = .2*9.81/(.2*.15)=65.4 A
current goes from left to right
2) using ampere's law
integral of B ds = u0 I enclosed = u0 * J* area
its a triangle so area = 4d*3d/2 =6 d^2
integral = 4*pi*10^(-7)*100*6*.02^2=3.016E-7
c) Vr = V0 e^(-tR/L)
.1 = e^(-t*3/2)
t=1.535 s