Answer:
The total charge on the surface of the conducting sphere is approximately 1.11 pico Coulombs.
Step-by-step explanation:
To calculate the total charge Q at the surface of a conducting sphere, we can use the formula relating electric field (E) and total charge (Q) for a conducting sphere:
E= Q / 4πϵ0 R²
where:
E is the electric field at the surface of the sphere.
Q is the total charge on the sphere.
ϵ0 is the vacuum permittivity (electric constant), which is approximately
8.854187817×10−12 F/m
R is the radius of the sphere.
In your case, the electric field at the surface of the sphere (E) is given as 100 V/m, and the radius (R) is 1 cm (or 0.01m).
Now, we can rearrange the formula to solve for the total charge (Q):
Q=4πϵ0ER²
Let's calculate the value:
Q=4π×8.854187817×10 -12 F/m×100 V/m×(0.01m) ²
Now, we can perform the calculation:
Q≈1.1132161×10 −12C.
To express this in pico Coulombs (pC), we need to move the decimal point 12 places to the right:
Q≈1.1132161pC.
So, the total charge on the surface of the conducting sphere is approximately 1.11 pico Coulombs.