...based on the angle.
1. The problem statement, all variables and given/known data
Figure 30-78 shows a wire that has been bent into a circular
arc of radius r = 24.0 cm, centered at O. A straight wire OP can be
rotated about O and makes sliding contact with the arc at P.
Another straight wire OQ completes the conducting loop. The
three wires have cross-sectional area 1.20 mm2 and resistivity
1.70 10^-8 Ωm, and the apparatus lies in a uniform magnetic
field of magnitude B = 0.150 T directed out of the figure.Wire OP
begins from rest at angle θ = 0 and has constant angular acceleration
of 12 rad/s2. As functions of θ (in rad), find (a) the loop’s
resistance and (b) the magnetic flux through the loop. (c) For what
u is the induced current maximum and (d) what is that maximum?
The image of the problem: http://ift.tt/1n5M40J
2. Relevant equations
Flux = ∫BdA
ε = -d(Flux)/dt
B = μ_0*i/2pi*r
3. The attempt at a solution
For part a), I solved using the resistivity equation, rho = R*A/l, with l = 2*r+ rθ, and solved for R.
For part b), I started with Flux = ∫BdA, took B outside of the integral (since it is uniform). I went to the integral solution for a circle, so I could just plug in the angle to get the area of the circle, which gave me 0.24^2/2 * θ = 2.88E-2*θ. That's my guess of where to go, anyhow.
What's throwing me off is I'm given the angular acceleration of the wire itself. I am at a loss of where to go. From worked out problems in the book, the velocity of the loop itself figures into the problem. But that's usually because they're trying to find the emf of the loop itself. Am I overthinking this second part? Should the solution just be Flux = B*2.88E-2*θ?
1. The problem statement, all variables and given/known data
Figure 30-78 shows a wire that has been bent into a circular
arc of radius r = 24.0 cm, centered at O. A straight wire OP can be
rotated about O and makes sliding contact with the arc at P.
Another straight wire OQ completes the conducting loop. The
three wires have cross-sectional area 1.20 mm2 and resistivity
1.70 10^-8 Ωm, and the apparatus lies in a uniform magnetic
field of magnitude B = 0.150 T directed out of the figure.Wire OP
begins from rest at angle θ = 0 and has constant angular acceleration
of 12 rad/s2. As functions of θ (in rad), find (a) the loop’s
resistance and (b) the magnetic flux through the loop. (c) For what
u is the induced current maximum and (d) what is that maximum?
The image of the problem: http://ift.tt/1n5M40J
2. Relevant equations
Flux = ∫BdA
ε = -d(Flux)/dt
B = μ_0*i/2pi*r
3. The attempt at a solution
For part a), I solved using the resistivity equation, rho = R*A/l, with l = 2*r+ rθ, and solved for R.
For part b), I started with Flux = ∫BdA, took B outside of the integral (since it is uniform). I went to the integral solution for a circle, so I could just plug in the angle to get the area of the circle, which gave me 0.24^2/2 * θ = 2.88E-2*θ. That's my guess of where to go, anyhow.
What's throwing me off is I'm given the angular acceleration of the wire itself. I am at a loss of where to go. From worked out problems in the book, the velocity of the loop itself figures into the problem. But that's usually because they're trying to find the emf of the loop itself. Am I overthinking this second part? Should the solution just be Flux = B*2.88E-2*θ?
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