Anonconducting sphere has radius r = 1.81 cm and uniformly distributed charge q = +2.08 fc. take the electric potential at the sphere's center to be v0 = 0. what is v at radial distance from the center (a) r = 1.20 cm and (b) r = r? (hint: see an expression for the electric field.)

a) V = -0.227 mV

b) V = -0.5169 mV

Explanation:

a)

Inside a sphere with a uniformly distributed charge density, electric field is radial and has a magnitude

E = (qr) / (4πε₀R³)

As we know that

V = -

By solving above equation, we get

V = (-qr²) / (8πε₀R³)

When

R = 1.81 cm

r = 1.2 cm

q = +2.80 fC

ε₀ = 8.85 × 10⁻¹²

V = (-2.80 × 10⁻¹⁵ × (1.2 × 10⁻²)²) / (8 × 3.14 × 8.85 × 10⁻¹² × (1.81 × 10⁻²)³)

V = -2.27 × 10⁻⁴ V

V = -0.227 mV

b)

When

r = R

R = 1.81 cm

q = +2.80 fC

ε₀ = 8.85 × 10⁻¹²

V = (-qR²) / (8πε₀R³)

V = (-q) / (8πε₀R)

V = (-2.80 × 10⁻¹⁵) / (8 × 3.14 × 8.85 × 10⁻¹² × (1.81 × 10⁻²))

V = -5.169 × 10⁻⁴ V

V = -0.5169 mV

i don't know that i agree with that but what's the question ?

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .