The magnetic force acting on the proton is
where
q is the proton charge
v is its speed
B is the intensity of the magnetic field
is the angle between the direction of v and B; since the proton is moving perpendicular to the magnetic field,
and
, so the force becomes
this force provides the centripetal force that keeps the proton in circular motion:
where the term on the left is the centripetal force, with
m being the mass of the proton
r the radius of its orbit
Re-arranging the previous equation, we can find the radius of the proton's orbit:
And now we can calculate the centripetal acceleration of the proton, which is given by
Answer:
a) Magnetic field strength, B = 2.397 * 10⁻⁷ T
b) Total energy density, U = 4.58 * 10⁻⁸ J/m³
c) Power flow per unit area, S = 13.71 W/m²
Explanation:
a) Electric field strength, E = 71.9 V/m
The relationship between the Electric field strength and the magnetic field strength in vacuum is:
E = Bc where c = 3.0 * 10⁸ m/s
71.9 = B * 3.0 * 10⁸
B = 71.9 / (3.0 * 10⁸)
B = 23.97 * 10⁻⁸
B = 2.397 * 10⁻⁷ T
b) Total Energy Density:
c)Power flow per unit area
Ok, assuming "mj" in the question is Megajoules MJ) you need a total amount of rotational kinetic energy in the fly wheel at the beginning of the trip that equals
(2.4e6 J/km)x(300 km)=7.2e8 J
The expression for rotational kinetic energy is
E = (1/2)Iω²
where I is the moment of inertia of the fly wheel and ω is the angular velocity.
So this comes down to finding the value of I that gives the required energy. We know the mass is 101kg. The formula for a solid cylinder's moment of inertia is
I = (1/2)mR²
We want (1/2)Iω² = 7.2e8 J and we know ω is limited to 470 revs/sec. However, ω must be in radians per second so multiply it by 2π to get
ω = 2953.1 rad/s
Now let's use this to solve the energy equation, E = (1/2)Iω², for I:
I = 2(7.2e8 J)/(2953.1 rad/s)² = 165.12 kg·m²
Now find the radius R,
165.12 kg·m² = (1/2)(101)R²,
√(2·165/101) = 1.807m
R = 1.807m
<span>force applied causes movement of an object in the same direction as the applied force.</span>
<span>The law of conservation of energy applies to a light bulb because the energy is being transformed into light and the light bulb is acting as a catalyst. The light bulb itself is not a form of energy, however when in combination with the electrical outlet to the bulb the electricity heats up the metal interior forming it into light. according to the law of conservation energy cannot be created or destroyed, but instead is formed into different kinds of energy. In relation to a light bulb electrical currents are forming heat energy by heating up the metal interior, then the bulb or glass around it allows to radiate light.</span>
