Please do A-D if possible. It would help a ton if someone could do all of it, bu
ID: 1777546 • Letter: P
Question
Please do A-D if possible. It would help a ton if someone could do all of it, but seeing as ive posted this once already without response for 12 hours, i assume its too much. Any help appreciated thanks
An electrical circuit is setup with 2 resistors, a switch, a battery, and a capacitor, as shown above. The conductive path from b on the switch is wired so that there are two rails resting in a uniform magnetic field B pointing out of the page, connected by a rod with mass m and length L in between them that can slide without friction on the rails. The switch is initially at b and has been in that positon for a long time. You can ignore any effects of the magnetic field on the current flow in the circuit and assume that the rails are infinitely long in both directions. 8 0, the switch is flipped from b to a. Find the current h() through [4 pts] At time resistor Ri as a function of time after the switch is flipped. a) b) [3 pts] After a long time, what is the voltage across the capacitor, C (write this below)? Draw a and- on the sides of the capacitor to indicate the sides that have higher and lower potential respectively [3 pts] After the switch has been at a for a long time, it is switched back to b. Draw an arrow next to the rod in the magnetic field to indicate the direction of the current and label it Irod. c) d) [4 pts] Find an expression for Irod(t) through the rod. You should restart the clock with 0 when the switch is flipped back from a to b [3 pts] Now, let's think about what the effect of the magnetic field is on the rod. Use the current direction that you found in (c) to get the direction of the force on the rod when a current flows through it. Does the force point to the right or to the left? [4 pts] Using everything you've done so far, write an equation for the force on the rod in the x-direction as a function of time, Fx(t). Take a force to the right as being positive e) f) g) [4 pts] Now that you know F(t), use that to find the velocity of the rod as a function of time if it is initially at rest. What speed does the rod have after a long time (i.e. t-> ) Hint: the change in momentum is equal to the integral of F dt.Explanation / Answer
a) I1 = (E/(R1 + R2))e-t/(C(R1+R2))
b) Vc = E(1 - e-t/(C(R1+R2))) (the side connected to +ve end of battery has higher potential
c) current Irod is from top to bottom
d) Irod = (E/R2)e-t/CR2
e) using FLHR, force on rod is to the left
f) Fx = -IrodLB = -(LBE/R2)e-t/CR2
g) mdv/dt = -(LBE/R2)e-t/CR2
v = (LBEC/m)e-t/CR2
after long time, v = 0 m/s