Our electrostatic generator, the Van de Graaff generator, has a spherical dome o

Question

Our electrostatic generator, the Van de Graaff generator, has a spherical dome of radius 12.5cm. If it were perfectly spherical (which it is not) and the air was dry, it would generate sparks when the field at the surface reached 3 × 106 N C . Compute the charge on the Van de Graaff generator at this surface field.

(a) 3.3 × 107C

(b) 6.5 × 107C

c) 5.2 × 106C

(d) 4.2 × 108C

(e) 2.2 × 109C

Consider three closed surfaces. Each surface contains a single point charge of charge Q. The first surface S1 is a sphere of radius r with the point charge at its center. The electric flux through this surface is 1. The second surface is a cube with side length r. The flux through this surface is 2. The third surface is a cube with side length r/2. The flux through the third surface is 3. The point charge is at the center of each surface. Select the relation below that best describes the relative size of the flux through the three surfaces. Select One of the Following:

(a) 1 = 2 = 3

(b) 1 = 2 < 3

(c) 1 > 2 > 3

(d) 2 < 1 < 3

(e) 2 > 1 > 3

Explanation / Answer

electric field = k * Q / r^2

3 * 10^6 = 9 * 10^9 * charge / 0.125^2

charge = 5.2 × 10^6 C

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