A magnetic field of magnitude B = 75 mT points at an angle = 30° from the normal
ID: 1794078 • Letter: A
Question
A magnetic field of magnitude B = 75 mT points at an angle = 30° from the normal of a circular loop of radius R = 20 mm as shown below. The loop has N = 500 turns.
a. Find the magnetic flux through the loop.
[Write your answer to 3 decimal places; don't forget that for units like m/s2, write as m/s2 (no spaces between the symbols).]
b. The magnitude of the magnetic field is decreasing with time. What direction of current will be induced in the coil of wire? Carefully explain your reasoning for this answer!
b1. What is the direction of the original magnetic field with respect to the figure (left, right, up, down, into, out of)?
b2. How is magnetic flux changing (increasing or decreasing)?
b3. Faraday's Law says a voltage will be induced to (reinforce / oppose) the change in flux.
b4. What is the direction of the INDUCED magnetic field with respect to the figure (left, right, up, down, into, out of)?
b5. What is the direction of the induced current in the wire (CW or CCW)?
c. The radius of the coil is decreasing steadily with time; the magnetic field is held constant. What direction of current will be induced in the coil of wire? Carefully explain your answer!
c1. What is the direction of the original magnetic field with respect to the figure (left, right, up, down, into, out of)?
c2. How is magnetic flux changing (increasing or decreasing)?
c3. Faraday's Law says a voltage will be induced to (reinforce / oppose) the change in flux.
c4. What is the direction of the INDUCED magnetic field with respect to the figure (left, right, up, down, into, out of)?
c5. What is the direction of the induced current in the wire (CW or CCW)?
Explanation / Answer
given
B = 75 mT
theta = 30 deg
R = 20 mm
N = 500 turns
a. MAgnetic flux = Bcos(theta)*pi*R^2 = 81620.97139 mT mm^2 = 8.162*10^-5 T m^2
b. for decreasing magnetic field, the current is such that the magnetic flux through the loop increases
hence induced current is in the anticlockwise direction as seen from the front
b1. direction of original magnetic field wrt figure = out of page
b2. magnetic flux is decreasing
b3. voltage will induce to oppose the change in flux
b4. induced magnetic field is out of the page
b5. induced current is anticlockwise
c. r is decreasing with time
c1. original magnetic field out of the page
c2. magnetic flux is decreasing
c3. voltage will induce to oppose the change in flux
c4. induced magnetic field is out of the page
e5. induced current is anticlockwise
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