A solid metal sphere of radius R1 50 cm has a charge of 20

A solid metal sphere of radius R_1 = 50 cm has a charge of +2.0 mu C. What is the strength of the electric field at the center of the sphere? What is the strength of the electric field 20 cm from the center of the sphere? What is the maximum strength of the electric field caused by the sphere? Where is it found? E = 7.l9x 10^4 N/C at r = R1 = 50 cm Graph the electric field E vs. radial distance r. What force would act on an excess electron (q = -1.60 times 10^-19 C) on the surface of the sphere? 1.15 times 10^-14 N [toward center of sphere] What is the strength of the electric field at a point 60 cm from the center of the sphere? 4.99 times 10^4 N/C What force would act on an alpha particle (q = +3.20 times 10^-19 C) located 60 cm from the center of the sphere? 1.60 x 10^-14 N [away from center of sphere]

Solution

Radius R = 50 cm = 0.5 m

Charge q = 2 x10 ^-6 C

(1).electric field inside the metal sphere is zero.

So, the strength of the electric field at the center of the sphere = 0

(2). The strength of the electric field 20 cm from the center of the sphere is also zero.

Since this point is also inside the sphere.

(3). The maximum strength of the electric field caused by the sphere E = Kq/R ²

Where K = Coulomb\'s constant = 8.99 x10 ⁹ Nm ²/C ²

Substitute values you get ,E =(8.99 x10 ⁹)(2 x10 ^-6 ) /0.5 ²

                                         = 71920 N/C

Electric field is maximum at the surface of the sphere.So,required distance = R = 50 cm

(5).Required force F = Eq

                             = 71920 x1.6 x10 ^-19

                             = 1.15 x10 ^-14 N

(6).The strength of the electric field at a point 60 cm from the center of the sphere E \' = Kq/r ²

Where r = 60 cm =0.6 m

Substitute values you get , E \'=(8.99 x10 ⁹)(2 x10 ^-6 ) / 0.6 ²

                                           = 4.9944 x10 ⁴ N/C

(7).Required force F \' = E \' q \'

Where q \' = charge of alpha particle

               = 2 x1.6 x10 ^-19 C

Substitute values you get , F \' = 4.9944 x10 ⁴ x 2 x1.6 x10 ^-19

                                            = 1.598 x10 ^-14 N

                                            = 1.6 x10 ^-14 N         ( two significant figures)