Answer:
The change in the charge on the positve plate when the Teflon is inserted is +2.5 nC.
Explanation:
- It can be showed that the capacitance of a parallel-plate capacitor, can be expresssed as follows:

- Where ε, is the dielectric constant of the material that fills the space between plates.
- When this space is filled with air, ε= ε₀ = 8,85*10⁻¹² F/m.
- At the same time, the capacitance of a capacitor, by definition, is as follows:

- If we insert a Teflon slab, in such a way that fills completely the gap between the plates, all other parameters being equal, if ε = 2*ε₀, this means that C₂ = 2* C₁. = 50 pF
- As V₂=V₁ (due to the capacitor remains connected to the same battery) the charge must be the double, so Q₂ = 2* Q₁ = 5 nC.
- So, the change in the charge of the positive plate is +2.5 nC.
In order to compute the final velocity of the trains, we may apply the principle of conservation of momentum which is:
initial momentum = final momentum
m₁v₁ = m₂v₂
The final mass of the trains will be:
10,000 + 10,000 = 20,000 kg
Substituting the values into the equation:
10,000 * 3 = 20,000 * v
v = 1.5 m/s
The final velocity of the trains will be 1.5 m/s
Answer:
Radius, r = 0.00523 meters
Explanation:
It is given that,
Magnetic field, 
Current in the toroid, I = 9.6 A
Number of turns, N = 6
We need to find the radius of the toroid. The magnetic field at the center of the toroid is given by :

r = 0.00523 m
or

So, the radius of the toroid is 0.00523 meters. Hence, this is the required solution.
Answer:
9.96x10^-20 kg-m/s
Explanation:
Momentum p is the product of mass and velocity, i.e
P = mv
Alpha particles, like helium nuclei, have a net spin of zero. Due to the mechanism of their production in standard alpha radioactive decay, alpha particles generally have a kinetic energy of about 5 MeV, and a velocity in the vicinity of 5% the speed of light.
From this we calculate the speed as
v = 5% 0f 3x10^8 m/s (speed of light)
v = 1.5x10^7 m/s
The mass of an alpha particle is approximately 6.64×10−27 kg
Therefore,
P = 1.5x10^7 x 6.64×10^−27
P = 9.96x10^-20 kg-m/s