Question

Modern Physics

Referring to the diagram, a long, thin wire carries a current I parallel to the z-axis â, = (0, 0, 1) (the direction of the current is assumed pointing out of the paper). The wire's axis is at the point with position vector ro = (xo, yo, 0),relative to the origin O.

The point P shown has position vector r = (x, y, 0), so that the position vector of P relative to the wire's axis is R.

Based on the Ampère's law, together with the vectors shown in the figure, we can know that the Cartesian components of the magnetic field H at Pare

Assume tuv w are the last four digits of your student number. For example, if your student number isC1700123, then t = 0, u =1. v =2 and w= 3.

A square boundary has its corners at the position vectors (10,10,0) m, (10,–10,0) m,(-10,–10,0)m and (-10,10,0) m. Two long, thin wires are fixed at (t+0.5,u +0.5,0) and(-v+0.5, -w+ 0.5,0) within it, with their axes parallel to the z-axis (0, 0, 1). The current /along each wire is 1 A, with the direction being pointing out of the paper. Using the equations given in the question to calculate the magnetic field H at the origin O.

Calculate the force per unit length F = I× B on each of the two wires (considering B= Ho H,where uo = 4r ×10 H/m); comment on your result in the context of Newton's third law.

Calculate the closed line integral q, H • de on the square boundary.  Verified     ### Question 52422  Modern Physics

1A cruiser moves away from the planet Hoth at a speed of 0.5c. A frigate follows, catching up at a speed of 0.25c as viewed from the cruiser. With what speed does the frigate appear to be moving according to observers on the planet? You should use the relativistic velocity transformation, clearly defining all the parameters used.
u^{\prime}=\frac{u-v}{1-\frac{u v}{c^{2}}}

### Question 44658  Modern Physics

Question 5: A spaceman goes out on a trip. First, he travels at 1/3 the speed of light in one direction. Then he comes back home at 2/3 of the speed of light. On Earth 9 years have passed,by how much has the spaceman aged? (Make sure you draw a space-time diagram).

### Question 44657  Modern Physics

Question 4: The typical pole for pole vaulting is 17 feet long. How fast would a pole vaulter have to run (in the direction of the pole) in order for a spectator sitting in the stands to see it 15feet long?

### Question 44656  Modern Physics

Question 3: If you weigh 150 lb in Chicago, how much do you weigh on top of mount Everest?(mount Everest is 8,848 m high).

### Question 44655  Modern Physics

Question 2: As a result of an explosion a stationary object breaks into three pieces. One piece flies east, one west and one north.
Explain why this is impossible.
Now, there are only two pieces; one flies east the other west. One piece weighs three times as much as the other. What is the ratio of the kinetic energies of the two pieces?

### Question 44654  Modern Physics

Question 1: The international Space Station (ISS) orbits the Earth once every 90 mins at an-altitude of 409 km. How high would it have to be in order to be to be in geosynchronous orbit?(make sure you show how you worked it out).

### Question 44179  Modern Physics

Question 6: A "star" made of ideal gas radiates away 10% of its energy while remaining in hydrostatic balance. Assuming that there are no nuclear reactions
Does the radius of the "star" increases or decreases? By how much?
Does the (average) temperature of the "star" increases or decreases? By how much?

### Question 44178  Modern Physics

5: There are two stars, one has twice the luminosity of the other and half the radius.
What is the ratio of their temperatures?
What is the ratio of their (apparent) brightness if the more luminous one is 100 times more distant than the other.

### Question 44177  Modern Physics

Question 4: According to general relativity people who live in hi-rise buildings age at differentrates depending on their floor.
Is that true?
Which floor ages fastest?

### Question 44176  Modern Physics

Question 3: Consider two time-like events P and Q. P is at the space-time origin P=(0,0); Q is at the space origin but one second later Q=(0,1).
Show that the order of events is preserved by all observers travelling at less than the speed of light.
Now events P and Q are space-like. P is still at the origin, but Q is simultaneous with P but one meter to the right 0=(1.0)
.Show that the order of events is not preserved by observers travelling at less than the speed of light.

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