Answer:
σ₁ =
C/m²
σ₂ =
C/m²
Explanation:
The given data :-
i) The radius of smaller sphere ( r ) = 5 cm.
ii) The radius of larger sphere ( R ) = 12 cm.
iii) The electric field at of larger sphere ( E₁ ) = 358 kV/m. = 358 * 1000 v/m


Q₁ = 572.8
C
Since the field inside a conductor is zero, therefore electric potential ( V ) is constant.
V = constant
∴

=
C
Surface charge density ( σ₁ ) for large sphere.
Area ( A₁ ) = 4 * π * R² = 4 * 3.14 * 0.12 = 0.180864 m².
σ₁ =
=
=
C/m².
Surface charge density ( σ₂ ) for smaller sphere.
Area ( A₂ ) = 4 * π * r² = 4 * 3.14 * 0.05² =0.0314 m².
σ₂ =
=
=
C/m²
Answer:

Explanation:
For the first ball, the moment of inertia and the kinetic energy is:


So, replacing, we get that:

At the same way, the moment of inertia and kinetic energy for second ball is:


So:

Then,
is equal to
, so:




Finally, solving for
, we get:

Answer:
4.17 m/s
Explanation:
To solve this problem, let's start by analyzing the vertical motion of the pea.
The initial vertical velocity of the pea is

Now we can solve the problem by applying the suvat equation:

where
is the vertical velocity when the pea hits the ceiling
is the acceleration of gravity
s = 1.90 is the distance from the ceiling
Solving for
,

Instead, the horizontal velocity remains constant during the whole motion, and it is given by

Therefore, the speed of the pea when it hits the ceiling is

Answer:
The flux through the surface of the cube is 
Solution:
As per the question:
Edge of the cube, a = 8.0 cm = 
Volume Charge density, 
Now,
To calculate the electric flux:
(1)
where
= electric flux
= permittivity of free space
Volume Charge density for the given case is given by the formula:
(2)
Volume of cube, 
Thus

Thus from eqn (2), the total charge is given by:


Now, substitute the value of 'q' in eqn (1):

Answer:

Explanation:
You can consider that the force that acts over the proton is the same to the force over the electron. This is because the electric force is given by:


where E is the constant electric field between the parallel plates, and is the same for both electron and proton. Also, the charge is the same.
by using the Newton second law for the proton, and by using kinematic equation for the calculation of the acceleration you can obtain:

(it has been used that vp^2 = v_o^2+2ad) where d is the separation of the plates, ap the acceleration of the proton, vp its velocity and mp its mass.
By doing the same for the electron you obtain:

we can equals these expressions for both proton and electron, because the forces qE are the same:
