A 1micro coulomb charge is uniformly distributed on a spherical shell by the equation x^2+ y^2+z^2=25 . What will be the intensity of electric field at a point (1,1,2)? plzz.explain.?

Question

Answer

Simple 1^2+1^2+2^2=6

Answer

Calculation of electric field intensity at point (1,1,2)

Given data

Charge distributed on a spherical shell = 1 micro coulomb

Equation of the spherical shell = x^2 + y^2 + z^2 = 25

Point at which electric field intensity needs to be calculated = (1,1,2)

Formula for electric field intensity

Electric field intensity is given by the formula:
E = kq/r^2
where k is Coulomb's constant, q is the charge and r is the distance between the point and the charge.

Calculation of electric field intensity

To calculate the electric field intensity at point (1,1,2), we need to follow these steps:

Calculate the distance between the point and the spherical shell

Calculate the charge per unit area of the spherical shell

Calculate the electric field intensity using the formula

Step 1: Calculate the distance between the point and the spherical shell

The distance between the point (1,1,2) and the spherical shell can be calculated using the distance formula:
d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
where (x1,y1,z1) = center of the spherical shell = (0,0,0)
and (x2,y2,z2) = point at which electric field intensity needs to be calculated = (1,1,2)

Substituting the values, we get:
d = sqrt((1-0)^2 + (1-0)^2 + (2-0)^2)
d = sqrt(6)

Step 2: Calculate the charge per unit area of the spherical shell

The charge per unit area of the spherical shell can be calculated using the formula:
sigma = q/A
where q is the total charge on the spherical shell and A is the surface area of the spherical shell.

The surface area of the spherical shell can be calculated using the formula:
A = 4*pi*r^2
where r is the radius of the spherical shell.

Substituting the values, we get:
A = 4*pi*5
A = 20*pi

Substituting the values, we get:
sigma = 1/(20*pi)

Step 3: Calculate the electric field intensity using the formula

Substituting the values in the formula, we get:
E = k*sigma*d
where k is Coulomb's constant.

Substituting the values, we get:
E = (9*10^9)*(1/(20*pi))*(sqrt(6))
E = 1.36*10^7 N/C

Therefore, the intensity of electric field at point (1,1,2) is 1.36*10^7 N/C.

Answer

Electric field will be zero because the point (1,1,2) lies within the shell

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