1) Consider three closed surfaces. Each surface contains a single point charge o

Question

1) 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.

(a)1 =2 =3

(b)1 =2 <3

(c)1 >2 >3

(d)2 <1 <3

(e)2 >1 >3

2. 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

Explanation / Answer

1. we know the electric flux = E.dA

E will be same for first two surfaces, but for cube having side r/2, E will be 4 times

area of sphere will be more than cube

and area of cube having side r/2 will be 1/4 times

(c) 1 >2 >3..........Ans.

2. We know that E = kQ/r2

hence Q = E.r2/k = 3 x 106 * 0.1252 / 9x109 = 5.20 x 10-6 C

(c) 5.2 × 106C..........Ans.

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