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A hollow, conducting sphere with an outer radius of 0.240 m and an inner radius of 0.200 m has a uniform surface charge density of +6.67 × 10^−6 C/m^2. A charge of -0.600 μC is now introduced into the cavity inside the sphere. Calculate the strength of the electric field at a distance 0.11 m from the center of the sphere.

2 Answers

5 votes

Final answer:

To calculate the strength of the electric field at a distance 0.11 m from the center of the hollow conducting sphere, we need to consider the electric field before and after introducing a charge inside the cavity. Before introducing the charge, the electric field is zero. After introducing the charge, we can calculate the electric field using Gauss's law.

Step-by-step explanation:

To calculate the electric field at a distance 0.11 m from the center of the conducting sphere, we need to consider two cases - before introducing the charge and after introducing the charge.

Before introducing the charge:

Since the conducting sphere has a uniform surface charge density of +6.67 × 10−6 C/m2, the electric field inside the sphere is zero. Therefore, the electric field at a distance 0.11 m from the center is also zero.

After introducing the charge:

When the charge of -0.600 μC is introduced into the cavity inside the sphere, it induces an equal and opposite charge on the inner surface of the sphere. This induced charge creates an electric field inside the sphere. The electric field due to the charge inside the sphere can be calculated using Gauss's law, which states that the electric field inside a uniformly charged spherical conductor is proportional to the charge enclosed within the Gaussian surface.

Since the charge inside the cavity has opposite sign, we can calculate the electric field at a distance 0.11 m from the center using the equation:

E = k * (q / r^2)

Where E is the electric field, k is the electrostatic constant, q is the charge inside the cavity, and r is the distance from the center of the sphere. Plugging in the values:

E = (9 * 10^9 N m2/C2) * (-0.600 * 10-6 C) / (0.11 m)2

Calculating this equation will give you the strength of the electric field at a distance 0.11 m from the center of the sphere.

User Abhinav Suman
by
5.4k points
5 votes

Answer: 446.28*10^3 N/C ( directed to center of the sphere)

Explanation: In order to explain this problem we have to use the electric field expression, which is given by:

E=k*q/r^2 where k is a constant equal 9*10^9 N/C^2*m^2, r is the distance from the charge to calculate the electric field.

Then we have,

E=(9*10^9*0.6*10^-6)/(0.11)^2= 446.28*10^3 N/C

Due to the negative point charge, the electric field is directed to the center of the sphere.

User Stew
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4.9k points