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The range of potential energies of the wire-field system for different orientations of the circle are -
θ U
0° 375 π x
90° 0
180° - 375 π x
We have current carrying wire in a form of a circle placed in a uniform magnetic field.
We have to the range of potential energies of the wire-field system for different orientations of the circle.
<h3>What is the formula to calculate the Magnetic Potential Energy?</h3>The formula to calculate the magnetic potential energy is -
U = M.B = MB cos
where -
M is the Dipole Moment.
B is the Magnetic Field Intensity.
According to the question, we have -
U = M.B = MB cos
We can write M = IA (I is current and A is cross sectional Area)
U = IAB cos
U = IπB cos
For = 0° →
U(Max) = MB cos(0) = MB = IπB = 5 × π ×
× 3 ×
=
375 π x .
For = 90° →
U = MB cos (90) = 0
For = 180° →
U(Min) = MB cos(0) = - MB = - IπB = - 5 × π ×
× 3 ×
=
- 375 π x .
Hence, the range of potential energies of the wire-field system for different orientations of the circle are -
θ U
0° 375 π x
90° 0
180° - 375 π x
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Answer:
<em>1360 cm</em>
Explanation:
<u>Oscillating Motion</u>
The shadow of a pendulum's x-coordinate is given by
x(t) = 34cos(πt)
Where 34 cm is the amplitude of the oscillation and is the angular frequency. Each time the shadow completes a whole cycle, it travels four times the amplitude: Twice from the peak to the valley and twice from the valley back to the peak. This means that each cycle the shadow travels 4*34=136 cm
Let's find the period of the oscillations. Given w, we can know the period by the formula
If we want to calculate the distance traveled by the shadow in 20 seconds, we can see it makes 20/2=10 full cycles, each one traveling 136 cm, thus the total distance traveled is 10*136=1360 cm