Suppose that the current in the solenoid is i(t. within the solenoid, but far from its ends, what is the magnetic field b(t due
to this current?
2 answers:
The magnetic field b(t) due to this current is
Suppose that the current in the solenoid is i(t). Within the solenoid, but far from its ends, what is the magnetic field B(t) due to this current?
The magnetic field is the area around a magnet where there is magnetic force. Moving electric charges can make magnetic fields. Then a solenoid is the long coil of wire wrapped in many turns. When a current passes through, it creates a nearly uniform magnetic field inside.
Solenoids can convert electric current to mechanical action, and so are very commonly used as switches
Even small solenoids can exert forces of a few newtons.
If we look through the solenoid far from ends, we can use Ampere's law to calculate the field strength. The magnetic field (deep) within the solenoid has a uniform value B, and outside the coils has value zero.
The magnetic field within a solenoid depends upon the current and density of turns. The magnetic field B(t) due to this current is . This is derived from Ampere's law used to calculate the strength of magnetic field.
Where is number of coils per meter and
is current through wire.
Learn more about the magnetic field
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1) Final kinetic energy of the cart: B) 50 J
2) Final speed of the cart: C) 3.2 m/s
3) Height reached along the ramp: A) 0.5 m
Explanation:
1)
We can solve this part of the problem by using the work-energy theorem, which states that the work done on an object is equal to the kinetic energy gained by the object itself. Mathematically:
where
W is the work done
is the final kinetic energy
is the initial kinetic energy
In this problem, the work done on the cart is
W = 50 J
And assuming it starts from rest, its initial kinetic energy is zero:
Therefore, the final kinetic energy is:
2)
The kinetic energy of an object is the energy possessed by an object due to its motion; it is calculated as
where
m is the mass of the object
v is its speed
For the cart in this problem, we have:
K = 50 J is its final kinetic energy
m = 10 kg is the cart
Therefore, solving the formula for v, we find its speed:
3)
We can think this problem in terms of conservation of energy. In fact, as the cart rolls up the ramp, its kinetic energy is converted into gravitational potential energy, which is given by
where
m is the mass
is the acceleration of gravity
h is the heigth of the cart
When the cart reaches the maximum height, all the kinetic energy has been converted into potential energy, so we can write:
Re-arranging,
And since we know the initial speed of the cart along the ramp,
v = 3.2 m/s
we can find the maximum height reached along the ramp:
Learn more about work, kinetic energy and potential energy:
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