A metal sphere of radius 10cm is given a electric charge find electric intensity and potential at a point whose distance from centre of sphere is:
a) 20cm b) 10cm and just outside c)5cm.
E=kQ/d^2 where d is >=10
c) inside, zero. No charge is enclosed.
To find the electric intensity and potential at different points, we need to use the concept of electric field and electric potential due to a charged sphere.
The electric field intensity due to a uniformly charged sphere is given by:
E = k * (Q / r^2),
where E is the electric field intensity, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), Q is the charge on the sphere, and r is the distance from the center of the sphere.
The electric potential due to a uniformly charged sphere is given by:
V = k * (Q / r),
where V is the electric potential.
a) To find the electric intensity and potential at a point whose distance from the center of the sphere is 20cm:
First, calculate the charge on the sphere. Let's assume the sphere has a charge of Q coulombs.
The radius of the sphere is given as 10 cm, so the distance from the center to the desired point is 20 cm. Substituting these values into the equation for electric field intensity:
E = k * (Q / r^2) = (9 x 10^9) * (Q / (0.2)^2)
Next, calculate the electric potential at this point using the formula:
V = k * (Q / r) = (9 x 10^9) * (Q / 0.2)
b) To find the electric intensity and potential at a point whose distance from the center of the sphere is 10 cm (just outside the sphere):
Since the distance is equal to the radius of the sphere, the point is just outside the sphere. The equation for the electric field intensity still holds:
E = k * (Q / r^2) = (9 x 10^9) * (Q / (0.1)^2)
Using the same formula as before, calculate the electric potential at this point:
V = k * (Q / r) = (9 x 10^9) * (Q / 0.1)
c) To find the electric intensity and potential at a point whose distance from the center of the sphere is 5 cm:
Substituting the values into the equation for electric field intensity:
E = k * (Q / r^2) = (9 x 10^9) * (Q / (0.05)^2)
And calculate the electric potential at this point:
V = k * (Q / r) = (9 x 10^9) * (Q / 0.05)
Remember, the values of Q and the resulting electric field intensity and potential depend on the charge given to the sphere. You would need to know the specific charge to get accurate values for E and V.