The number of excess electrons needed to be distributed uniformly in the sphere to produce the given electric field is 1.69*10^(10).
What is an electric field?
The electric force exerted on a unit charge is called the electric field.
For a sphere of uniform charge density, the magnitude of the electric field on its surface is given by,
E=k*q/r^2
where E is the magnitude of the electric field, k is the coulomb's constant which has a value of 9*10^9 N m^(2) C^(-2), and q is the total charge of the sphere, and r is the radius of the sphere.
The radius of the sphere is half of the diameter. Given the diameter of the sphere is 26.0 m, the radius of the sphere r=26.0/2 cm or r=13.0 cm.
It is given that E=1440 N/C, r=13.0 cm, and the value of k is 9*10^9 N m^(2) C^(-2). Substitute these values in the formula of the electric field and solve it to get the value of the total charge on the sphere.
Note: 1 cm = 0.01 m.
1440 (N/C)= (9*10^9 N m^(2) C^(-2))*q/( 13 cm)^2
1440 (N/C)= (9*10^9 N m^(2) C^(-2))*q/( 13*0.01 m)^2
1440 ( N/C)= (532.54*10^(9) N C^(-2))*q
q=1440/(532.54*10^(9)) C
q=2.704*10^(-9) C
Since the charge is quantized, the total charge inside the sphere is the integral multiple of an elementary charge. In the given case, the value of that elementary charge is 1.6*10^(-19) C. The total charge is then given by,
q=ne
where q is the total charge, n is the number of elementary charges and e is the value of the elementary charge.
The value of q is 2.704*10^(-9) C and the value of e is 1.6*10^(-19) C.
Substitute these values in the formula of total charge and solve it to get the number of elementary charges.
2.704*10^(-9) C =n*1.6*10^(-19) C
n=2.704*10^(-9)/ 1.6*10^(-19)
n=1.69*10^(10)
Learn more about the electric field here:
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