0.017s
Explanation:
Given parameter
Distance = 5000km = 5 x 10⁶m
Unknown:
time taken = ?
Solution:
We use the normal speed equation to solve this problem as we take the speed of the wave to be 3 x 10⁸m/s.
Speed =
Inputting the parameters:
Time taken =
Time taken = = 0.017s
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1. The magnitude of the magnetic field doubles
Explanation: the intensity of the magnetic field produced by a current-carrying wire is given by:
where is the vacuum permeability, I is the current in the wire, r is the distance from the wire.
As we see from the formula, the intensity of the magnetic field is directly proportional to the current: if the current increases from 5 A to 10 A, it means it doubles, so the magnetic field doubles as well.
2. The magnitude of the magnetic field halves
Explanation: the intensity of the magnetic field produced by a current-carrying wire is given by:
We see that the magnitude of the magnetic field is inversely proportional to the distance from the wire (r). In this case, the distance of the particle is changed from 10 cm to 20 cm, so it is doubled: therefore, the magnitude of the field will become half of the initial value.
3. The force reverses direction
Explanation: the force exerted on a charged particle in a magnetic field is:
where q is the charge, v is the speed of the particle, B is the magnetic field intensity and the angle between the direction of v and B. If the charge of the particle is switched from 2 µC to –2µC, the magnitude of the force does not change (because the absolute value of q does not change), however the charge q gets a negative sign (-), so the sign of the force changes and gets a negative sign too, so the force reverses direction.
(a)
The resistance of the rod is given by:
(1)
where
is the material resistivity
L = 1.20 m is the length of the rod
A is the cross-sectional area
The radius of the rod is half the diameter: , so the cross-sectional area is
The resistance at 20°C can be found by using Ohm's law. In fact, we know:
- The voltage at this temperature is V = 15.0 V
- The current at this temperature is I = 18.6 A
So, the resistance is
And now we can re-arrange the eq.(1) to solve for the resistivity:
(b)
First of all, let's find the new resistance of the wire at 92.0°C. In this case, the current is
I = 17.5 A
So the resistance is
The equation that gives the change in resistance as a function of the temperature is
where
is the resistance at the new temperature (92.0°C)
is the resistance at the original temperature (20.0°C)
is the temperature coefficient of resistivity
Solving the formula for , we find