A slab of insulating material has a nonuniform positive charge density ρ = Cx^2, where x is measured from the center of the slab as shown in Figure and C is constant. The slab is infinite in the y and z-direction. Derive an expression for the electric field in

the exterior regions, x> d/2

the interior regions, -d/2 <x < d/2

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Uttam SaikiaLv10

17 Nov 2020

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A slab of insulating material of uniform thickness d, lying between -d/2 to +d/2 along the x-axis, extends infinitely in the y and z directions. The slab has a uniform charge density ρ. The electric field is zero in the middle of the slab, at x = 0.

(a) What is E_out, the magnitude of the electric field outside the slab?

(b)What is E_in, the magnitude of the electric field inside the slab as a function of x?

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An infinite metal slab is located perpendicular to thex-axis, between x = 0 and x = 2.0 cm(see figure). The slab has a surface charge density of +4.8 Ã 10-6C/m2 on each side.

(a) Find the magnitude of the potentialdifference between x = 0 and x = 8 cm.

|V(8 cm) - V(0)| =V

For parts (b) and (c), take the potential to be 0 at x= 0.

(b) What is the potential at x = 2.0 cm?.

V(2.0 cm) = V *

V(8 cm) = V

HELP: The slab is made of aconducting material. Also, watch the signs: theelectric field always points in the direction of decreasingpotential.

For parts (d) and (e), take the potential to be 0 at x= -8 cm.

(d) What is the potential at x = 2.0 cm?.

V(2.0 cm) = V

(e) What is the potential at x = 10 cm?.

V(10 cm) = V

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A solid insulating sphere of radius R has a nonuniform charge density that varies with r according to the expression ρ = Ar 2, Where A is a constant and r<R is measured from the centre of the sphere.

(a). Show that the magnitude of the electric field outside (r > R) the sphere is