21.49 .. a charge of -6.50 nc is spread uniformly over the surface of one face of a nonconducting disk of radius 1.25 cm. (a) find the magnitude and direction of the electric field this disk produces at a point p on the axis of the disk a distance of 2.00 cm from its center. (b) suppose that the charge were all pushed away from the center and distributed uniformly on the outer rim of the disk. find the magnitude and direction of the electric field at point p. (c) if the charge is all brought to the center of the disk, find the magnitude and direction of the electric field at point p. (d) why is the field in part (a) stronger than the field in part (b)? why is the field in part (c) the strongest of the three fields?

Explanation:

It is given that,

Charge,

Radius of the disk, R = 1.25 cm = 0.0125 m

(a) Electric field at a distance of 2 cm from the center of the disk. It can be calculated using the formula as :

Where

is the surface charged density,

So,  

The direction of electric field is outwards.

(b) Suppose that the charge were all pushed away from the center and distributed uniformly on the outer rim of the disk. So, the electric field due to the ring is :

The direction of electric field is outwards.

(c) If the charge is all brought to the center of the disk, The electric field at the center of disk is given by :

(d) he field in part (a) stronger than the field in part (b). This is due to the reason that the charge at the center of the ring is 0.

(e) The field in part (c) the strongest of the three fields because the for a point charge the charges are at same distances.

ammonium chloride & tallow

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .