22.45 · Concentric Spherical Shells. A small conductingspherical shell with inner radius a and outer radius b is concen-tric with a larger conducting spherical shell with inner radius cand outer radius d (Fig. P22.45). The inner shell has total charge+2q, and the outer shell has charge +4q. Figure P22.45(a) Calculate the clectric field Ë (magni-tude and direction) in terms of q and thedistance r from the common center of thetwo shells for (1) r< a; (ii) a d.Graph the radial component ofÉ as afunction of r. (b) What is the total chargeon the (i) inner surface of the small shell;(ii) outer surface of the small shell; (iii) in-ner surface of the large shell; (iv) outer surface of the large shell?

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22.45 · Concentric Spherical Shells. A small conducting spherical shell with inner radius a and outer radius b is concen- tric with a larger conducting spherical shell with inner radius c and outer radius d (Fig. P22.45). The inner shell has total charge +2q, and the outer shell has charge +4q. Figure P22.45 (a) Calculate the clectric field É (magni- tude and direction) in terms of q and the distance r from the common center of the two shells for (i) r< a, (ii) a < r< b, (iii) b d. Graph the radial component of É as a function of r. (b) What is the total charge on the (i) inner surface of the small shell; (ii) outer surface of the small shell; (iii) in- ner surface of the large shell; (iv) outer surface of the large shell?

22.45 · Concentric Spherical Shells. A small conducting spherical shell with inner radius a and outer radius b is concen- tric with a larger conducting spherical shell with inner radius c and outer radius d (Fig. P22.45). The inner shell has total charge +2q, and the outer shell has charge +4q. Figure P22.45 (a) Calculate the clectric field É (magni- tude and direction) in terms of q and the distance r from the common center of the two shells for (i) r< a, (ii) a < r< b, (iii) b d. Graph the radial component of É as a function of r. (b) What is the total charge on the (i) inner surface of the small shell; (ii) outer surface of the small shell; (iii) in- ner surface of the large shell; (iv) outer surface of the large shell?

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Chapter1: Units, Trigonometry. And Vectors

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Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

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22.45 · Concentric Spherical Shells. A small conducting
spherical shell with inner radius a and outer radius b is concen-
tric with a larger conducting spherical shell with inner radius c
and outer radius d (Fig. P22.45). The inner shell has total charge
+2q, and the outer shell has charge +4q. Figure P22.45
(a) Calculate the clectric field Ë (magni-
tude and direction) in terms of q and the
distance r from the common center of the
two shells for (1) r< a; (ii) a <r<b;
(iii) b <r<c; (iv) c <r< d; (v) r > d.
Graph the radial component ofÉ as a
function of r. (b) What is the total charge
on the (i) inner surface of the small shell;
(ii) outer surface of the small shell; (iii) in-
ner surface of the large shell; (iv) outer surface of the large shell?

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