(a) What is the electric field at location A (6 cm to the right of the center of

Question

(a) What is the electric field at location A (6 cm to the right of the center of the large sphere)? Neglect the small contribution of the polarized molecules in the plastic, because the shells are very thin and don't contain much matter.

< 1     , 2     , 3     > N/C

(b) What is the electric field at location B (15 cm above the center of the small sphere)? Again, neglect the small contribution of the polarized molecules in the plastic, because the shells are very thin and don't contain much matter.

<       4     ,     5     , 6                   > N/C

(c) What is the force on an electron placed at location B?

<      7     ,     8     , 9             > N

Explanation / Answer

a) For point A, there wont be any effect due to the charge on the surface of bigger shell as for any point inside the shell, the total electric flux through any gaussian surface (say shell with radius OA) will be zero due to this shell. However, there will be field due to the second shell.

Hence electric field at A = Ea = 9 * 10^9 * (1 * 10^(-9)) / (0.25 - 0.06)^2

= (249.308, 0, 0) N/C (this will be attractive field towards the second sphere for a unit positive charge placed at A).

b) For point B, both spheres will contribute to electric field.

Eb1 = 9 * 10^9 * 7 * 10^(-9) / (0.292)^2 (distance of B from centre of first sphere can be calculated to be 0.292m from given data)

=> Eb1 = 738.882 N/C and this will be along the straight line joining the origin and B acting away from B, making an angle of ? = arctan(15/25) = 30.96deg with +ve x-axis counter-clockwise.

Similarly, Eb2 = 9 * 10^9 * 1 * 10^(-9) / (0.15)^2

=> Eb2 = 400 N/C and this will be along the straight line joining the origin and B acting towards centre of second shell from B. i.e., this will be acting along -ve y-axis direction.

Hence the x-component of resultant field Ebx = Eb1 * Cos(?) + 0 (since Eb2 wont have any x-component).

=> Ebx = 633.614 N/C

The y-component of resultant field Eby = Eb1 * Sin(?) + Eb2

=> Eby = 380.111 - 400 (since Eb2 will be along -ve y-axis and Eb1y will be along +ve y-axis.

=> Eby = - 19.889 N/C (along -ve y-axis)

Hence the component of resultant electric field = Eb = sqrt(Ebx^2 + Eby^2)

= 633.926 N/C

making an angle of ? = arctan(Eby/Ebx) = -1.798deg with +ve xaxis = 358.202deg with +ve x-axis counter-clockwise.

In terms of vector representation, feild = Eb = (633.926, -19.889, 0) N/C

c) Force acting on an electron placed at this point is given by

F = e * E = 1.6 * 10^(-19) * (633.926, -19.889, 0)

= (1014.282 * 10^(-19), -31.8224 * 10^(-19), 0) N

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