Question

Проводящий шарик радиусом 2,5 см, погруженный в глицерин, имеет заряд, поверхностная плотность которого 1,3*10^-5 Кл/м^2. Определить напряженность электрического поля этого заряда в точке, удаленной от поверхности шарика на 7,5 см.

Answer 1

R1=2,5 см=0,025 м
ε= 41
σ=1,3*10^-5 Кл/м^2
r2= 7,5 см=0,075 м
Е-?   

Е=kq/(εr), σ=q/S=q/(4πr²)⇒ q=σ*4πr², r=r1+r2=0,1 м, E=kσ*4πr²/(εr)=kσ*4πr/ε,
E=9*10^9*1,3*10^-5*4*3,14*0,1/41= 0,36*10^4 Н/Кл.

Answer 2

Calculation of Electric Field Intensity

To determine the electric field intensity at a point located 7.5 cm away from the surface of a conducting sphere with a radius of 2.5 cm and a surface charge density of 1.3 * 10^-5 C/m^2, we can use the formula for the electric field intensity due to a uniformly charged sphere.

The formula for the electric field intensity at a point outside a uniformly charged sphere is given by:

E = k * (Q / r^2)

Where: - E is the electric field intensity - k is the electrostatic constant (k = 9 * 10^9 Nm^2/C^2) - Q is the total charge of the sphere - r is the distance from the center of the sphere to the point where the electric field is being measured

In this case, the charge on the sphere can be calculated by multiplying the surface charge density by the surface area of the sphere.

The surface area of a sphere is given by the formula:

A = 4πr^2

Where: - A is the surface area of the sphere - r is the radius of the sphere

Let's calculate the charge on the sphere and then use it to find the electric field intensity at the given point.

Calculation Steps:

1. Calculate the charge on the sphere using the surface charge density and the surface area of the sphere. 2. Substitute the values into the formula for electric field intensity to find the answer.

Step 1: Calculate the charge on the sphere

The surface area of the sphere can be calculated using the formula:

A = 4πr^2

Substituting the given radius of the sphere (2.5 cm) into the formula:

A = 4π(2.5 cm)^2

Calculating the surface area:

A = 4π(6.25 cm^2) = 25π cm^2

The charge on the sphere can be calculated by multiplying the surface charge density by the surface area:

Q = (1.3 * 10^-5 C/m^2) * (25π cm^2)

Converting the charge to Coulombs:

Q = (1.3 * 10^-5 C/m^2) * (25π cm^2) * (10^-4 m^2/cm^2)

Q = 3.25π * 10^-4 C

Step 2: Calculate the electric field intensity at the given point

Now that we have the charge on the sphere (Q) and the distance from the center of the sphere to the point where the electric field is being measured (r = 7.5 cm), we can substitute these values into the formula for electric field intensity:

E = k * (Q / r^2)

Substituting the values:

E = (9 * 10^9 Nm^2/C^2) * (3.25π * 10^-4 C) / (7.5 cm)^2

Converting the distance to meters:

E = (9 * 10^9 Nm^2/C^2) * (3.25π * 10^-4 C) / (7.5 * 10^-2 m)^2

Calculating the electric field intensity:

E ≈ 1.45 * 10^4 N/C

Therefore, the electric field intensity at a point located 7.5 cm away from the surface of the conducting sphere is approximately 1.45 * 10^4 N/C.

Please note that the above calculation assumes that the conducting sphere is a solid, non-hollow sphere. If the sphere is hollow, the calculation would be different.