Table of Contents
What is the formula of hollow sphere?
To determine the volume of a sphere, we use the formula 4/3πr^3. So, to find the volume of a hollow sphere, we must subtract the volume of the hollow region from the volume of the overall sphere. Let’s call the radius of the overall sphere r1 and the radius of the hollowed region r2. Thus, we get 4/3π*r1^3 – 4/3π*r2^3.
What is the surface charge density on the outer surface of the hollow sphere?
Surface charge density on outer surface =4πr(Q+q)
How do you calculate Q Enclosed?
q (coulombs enclosed) = D x 4 r2. The lines of flux contributing to the flux density are those that leave the sphere perpendicular to the surface of the sphere.
What is the formula for density of a sphere?
Knowing radius, you can count the volume of a sphere with the equation volume = (4/3) × π × r3. Then, using the density formula density = mass/volume, you can count the mass by multiplying density and volume: mass = volume × density. You can also use a combined formula: mass = (4/3) × π × r3 × density.
What is hollow sphere in physics?
A hollow sphere is a sphere that has been thinned out, has space and a cavity inside and is not solid.
What is the total area of hollow sphere?
What is the total surface area of a hollow hemisphere? The total surface area of a hollow hemisphere whose inner and outer radii are r1 and r2, respectively, is given by 2 (r22 + r12) + (r22 – r12) square units.
What is a hollow sphere in maths?
A hollow sphere is what is left of a sphere with radius r2, when a sphere with radius r1 has been removed from it, the two spheres having the same centre and r1 < r2.
Is it total surface area of a hollow sphere?
The total surface area of a hollow sphere is equal to the CSA of hollow sphere as a hollow sphere has only one surface that constitutes it.
What is the charge density on the inner surface of the shell?
surface charge density at the inner surface of the shell is given by the realation,
`sigma_(1)=(“Total charge”)/(“inner surface area”)=(-q)/(4pir_(1)^(2))….. (i)`
A charge of +q is induced on the outer surface of the shell. a charge of magnitude Q is place on the outer surface of the shell .
What is the new charge density on the outside of the sphere?
(a) The new charge density on the outside of the sphere is 5.733 × 1 0 − 6 C / m 2 5.733 times 10^-6 mathrm~C/m^2 5.733×10−6 C/m2.
Why electric field inside a hollow sphere is zero?
As there are no charges inside the hollow conducting sphere, as all charges reside on it surface. So, electric field inside the hollow conducting sphere is zero.
What is Q in gauss’s law?
The Gauss law formula is expressed by; ϕ = Q/ϵ0. Where, Q = total charge within the given surface, ε0 = the electric constant.
Why do we use gauss law?
Gauss’s Law is a general law applying to any closed surface. It is an important tool since it permits the assessment of the amount of enclosed charge by mapping the field on a surface outside the charge distribution. For geometries of sufficient symmetry, it simplifies the calculation of the electric field.
How do you use the gauss theorem?
According to Gauss’s law, the flux through a closed surface is equal to the total charge enclosed within the closed surface divided by the permittivity of vacuum ϵ0. Let qenc be the total charge enclosed inside the distance r from the origin, which is the space inside the Gaussian spherical surface of radius r.
How do you find density using diameter?
The density can be found with the formula, density equals mass over volume (d = m/v): The mass is given m = 540 grams, you can plug that into the formula first. H is the height or length, R is the radius or half of the diameter, and π can remain or it can be rounded to 3.14.
How do you find density with height and diameter?
To calculate the density of a cylinder, follow these steps: Measure the mass m of the cylinder if it is not already known. Determine the cylinder’s volume V from its radius r and height h using the formula V = πr²h . Divide the cylinder’s mass by its volume to get its density ρ = m/v .
How do you find the radius of a sphere given the density?
How do you find the inertia of a hollow sphere?
Figure 1: The rotational inertia of a hollow sphere is given by I=23MR2 I = 2 3 M R 2 and the rotational inertia of a solid ball is given by 25MR2 2 5 M R 2 .
Is Shell and hollow sphere the same?
Shell and hollow sphere are one and the same thing.. Shells are like layers of a sphere at different distance from the center. If you consider (hypothetically) a spherical onion, Its body is made of different concentric layers, each one enclosing the other.
What is the difference between hollow sphere and solid sphere?
The solid sphere is has the moment of inertia as 52mr2 and that of hollow sphere is 32mr2. The moment of inertia for hollow sphere is larger thereby having a greater resistance to motion. Thus the solid sphere will have greater speed.
What is the total surface area and curved surface area of a hollow semi sphere?
The total surface area of a hemisphere = 3πr2, where ‘r’ is the radius of the hemisphere. The curved surface area of a hemisphere = 2πr2, where ‘r’ is the radius of the hemisphere.
How do you find the volume of a hollow cylinder?
The formula to calculate the volume of a hollow cylinder is given as, Volume of hollow cylinder = π (R2 – r2) h cubic units, where, ‘R’ is the outer radius, ‘r’ is the inner radius, and, ‘h’ is the height of the hollow cylinder.
What is the formula for total surface area of a hemisphere?
The total surface area of a hemisphere = 3πr2 square units Where π is a constant whose value is equal to 3.14 approximately.
Why is the formula for the volume of a sphere?
Volume of a sphere = 4/3 πr3 If you consider a circle and a sphere, both are round. The difference between the two shapes is that a circle is a two-dimensional shape and a sphere is a three-dimensional shape which is the reason that we can measure the Volume and area of a Sphere.