10. The maximum electric intensity outsis the surface of an isolated spherical conductor is 3x 10%/m. Calculate the maximum charge on the sphere and the maximum energy
stored, if its radius is 0.2 m. 11. Calculate the value of two equal charges, if they repel each other with a force of 0.1N when situled 50 cm apart in a vacuum
10. Given that the maximum electric intensity outside the surface of the conductor is 3 x 10^6 N/m and the radius of the sphere is 0.2 m, we can use Gauss's law to find the maximum charge on the sphere.
The electric field at a distance r from the center of a uniformly charged spherical conductor of radius R is given by:
E = k * Q / r^2
where k is the Coulomb's constant (k = 8.9875 x 10^9 N m^2/C^2), Q is the charge on the sphere, and r is the distance from the center of the sphere.
Given that E = 3 x 10^6 N/m and r = 0.2 m, we can plug in these values to find Q:
Q = E * 4 * π * (0.2)^2 / k
Q = 3 x 10^6 * 4 * π * 0.04 / 8.9875 x 10^9
Q ≈ 5.3 x 10^-7 C
To calculate the maximum stored energy, we can use the formula for the energy stored in a charged spherical conductor:
U = Q^2 / (2C)
where C is the capacitance of the sphere. The capacitance of a spherical conductor is given by:
C = 4πε₀R
where ε₀ is the permittivity of free space (ε₀ = 8.854 x 10^-12 F/m) and R is the radius of the sphere.
Given that R = 0.2 m, we can calculate the capacitance:
C = 4 * π * 8.854 x 10^-12 * 0.2
C ≈ 2.23 x 10^-11 F
Now we can plug in the values of Q and C to find the maximum stored energy:
U = (5.3 x 10^-7)^2 / (2 * 2.23 x 10^-11)
U ≈ 0.061 J
Therefore, the maximum charge on the sphere is approximately 5.3 x 10^-7 C and the maximum stored energy is approximately 0.061 J.
11. The force between two charges q1 and q2 separated by a distance r is given by Coulomb's law:
F = k * |q1 * q2| / r^2
where k is the Coulomb's constant (k = 8.9875 x 10^9 N m^2/C^2).
Given that q1 = q2 = q, F = 0.1 N, and r = 50 cm = 0.5 m, we can plug in these values to find the charge of each particle:
0.1 = 8.9875 x 10^9 * q^2 / 0.5^2
0.1 = 8.9875 x 10^9 * q^2 / 0.25
0.1 = 35.95 x 10^9 * q^2
q^2 = 0.1 / 35.95 x 10^9
q^2 ≈ 2.7864 x 10^-13
q ≈ √(2.7864 x 10^-13)
q ≈ 5.27 x 10^-7 C
Therefore, the value of each charge is approximately 5.27 x 10^-7 C.