Question

A solid non-conducting sphere (R = 10 cm) has a charge of uniform density 50 nC/m3 uniformly distributed throughout its volume. (a) Determine the magnitude of the electric field 20 cm from the center of the sphere. (b) Determine the magnitude of the electric field 5 cm from the center of the sphere. Hint: first calculate the charges inside the assumed Gaussian surfaces, assume π = 3. Answer: 45 N/C, 90 N/C.

Answer 1

Let us first sind the total charge on solid sphere. given volume charse density (8) = 50 ncmo = 50x100 cm 8= total charge (Q) volume of sphere (v) wolume of sphere - 4 R- 4 x 3x (10x172)3 R = Radius of sphere = 10x10²m V = 4000x100m² Q=8V = 50x109 x 4000 x 100 Q = 2 X10' past a:- Here, ure want to calculate electric field at a distance 8= 20cm from the centre of sphere. Electric field at a point outside the solid sphere can be determined by considering the whole Charge Q is concentrated at the origin. 45N/c. (20 x 18 22 E = 45 - 9X10°x 2x1000 where, I = 9X100 Nm

Part b) Here we are calculating electric field at a distance 8 = 5 cm = 5x 10²m.i.e inside the sphere In this case draw the gaussian sphere of radius 8=5cm. According to the Gauss theorem. E 4T ² - 4 E = 1 1/2 To Gaussian Sphere q' = charge enclosed by the As charge is uniformly Gaussian sphere, distributed, (e) is constant everywhere, : E = 4T60 82 isan 4116 8² R3 2R3 4162 R3 = 2X10 X 9X10' x 5X102 = 0.09 X109 NIC 10 x 10273 JE = go well