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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.?
Most Upvoted Answer
A 1micro coulomb charge is uniformly distributed on a spherical shell ...
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:

  1. Calculate the distance between the point and the spherical shell

  2. Calculate the charge per unit area of the spherical shell

  3. 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.
Community Answer
A 1micro coulomb charge is uniformly distributed on a spherical shell ...
Electric field will be zero because the point (1,1,2) lies within the shell

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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.?
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