Question

In: Physics

Two 2.0-cm-diameter insulating spheres have a 5.60 cm space between them. One sphere is charged to...

Two 2.0-cm-diameter insulating spheres have a 5.60 cm space between them. One sphere is charged to + 40.0 nC , the other to - 60.0 nC .

Part A

What is the electric field strength at the midpoint between the two spheres?

Expert Solution

Given:

diameter of spheres d = 2.0cm

radius of the spheres r = d/2

= 1cm

= 1*10^-2 m

charge on sphere 1 q1 = 40*10^-9 C

charge on sphere 2 q2 = -60 *10^-9 C

distance between the spheres d = 5.60*10^-2 m
midpoint p =2.80*10^-2 m

Electric field strength due to sphere1 at point p

total distance to point p = (2.80*10^-2)+ 1*10^-2

=3.8*10^-2 m

Electric field E₁ = kq₁/r^2.......(1)

= (9*10^9)(40*10^-9)/(3.8*10^-2)^2

= 24.9*10⁴N/C

Electric field strength due to sphere 2 at point p

total distance to point p = (2.8*10^-2)+ 1*10^-2

= 3.8*10^-2 m

Electric field E₂ = kq₂/r^2.......(1)

= (9*10^9)(60*10^-9)/(3.8*10^-2)^2

= 37.4*10⁴ N/C

total electric field strength at point p E = E₁+E₂

= 62.3*10⁴N/C

˜62.3*10⁴N/C

genius_generous answered 1 year ago

Two 2.0-cm-diameter insulating spheres have a 7.00 cm space between them. One sphere is charged to...

Two 2.0-cm-diameter insulating spheres have a 7.00 cm space between them. One sphere is charged to + 70.0 nC , the other to - 79.0 nC . Part A What is the electric field strength at the midpoint between the two spheres? Express your answer with the appropriate units.

There are two identical, positively charged conducting spheres fixed in space. The spheres are 43.0 cm...

There are two identical, positively charged conducting spheres fixed in space. The spheres are 43.0 cm apart (center to center) and repel each other with an electrostatic force of F1 = 0.0675 N. Then, a thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed the spheres still repel but with a force of F2 = 0.100 N. Using this information, find the initial charge on each sphere, q1 and q2 if initially...

There are two identical, positively charged conducting spheres fixed in space. The spheres are 41.0 cm...

There are two identical, positively charged conducting spheres fixed in space. The spheres are 41.0 cm apart (center to center) and repel each other with an electrostatic force of F1 = 0.0600 N. Then, a thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed the spheres still repel but with a force of F2 = 0.115 N. Using this information, find the initial charge on each sphere, q1 and q2 if initially...

There are two identical, positively charged conducting spheres fixed in space. The spheres are 34.8 cm...

There are two identical, positively charged conducting spheres fixed in space. The spheres are 34.8 cm apart (center to center) and repel each other with an electrostatic force of ?1=0.0765 N . A thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed, the spheres still repel, but with a force of ?2=0.100 N . The Coulomb force constant is ?=1/(4??0)=8.99×109 N⋅m2/C2 . Using this information, find the initial charge on each sphere,...

Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.250 kg and 0.700 kg,...

Two insulating spheres have radii 0.300 cm and 0.500 cm, masses 0.250 kg and 0.700 kg, and uniformly distributed charges of -2.00 µC and 3.00 µC. They are released from rest when their centers are separated by 1.00 m. (a) How fast will each be moving when they collide? (Hint: Consider conservation of energy and of linear momentum.) m/s (lighter sphere) m/s (heavier sphere) (b) If the spheres were conductors, would the speeds be greater or less than those calculated...

There are two identical, positively charged conducting spheres fixed in space. The spheres are 39.6 cm39.6...

There are two identical, positively charged conducting spheres fixed in space. The spheres are 39.6 cm39.6 cm apart (center to center) and repel each other with an electrostatic force of ?1=0.0675 NF1=0.0675 N . A thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed, the spheres still repel, but with a force of ?2=0.115 NF2=0.115 N . The Coulomb force constant is ?=1/(4??0)=8.99×109 N⋅m2/C2k=1/(4πϵ0)=8.99×109 N⋅m2/C2 . Using this information, find the initial...

There are two identical, positively charged conducting spheres fixed in space. The spheres are 38.2 cm38.2...

There are two identical, positively charged conducting spheres fixed in space. The spheres are 38.2 cm38.2 cm apart (center to center) and repel each other with an electrostatic force of ?1=0.0705 NF1=0.0705 N . A thin conducting wire connects the spheres, redistributing the charge on each sphere. When the wire is removed, the spheres still repel, but with a force of ?2=0.100 NF2=0.100 N . The Coulomb force constant is ?=1/(4??0)=8.99×109 N⋅m2/C2k=1/(4πϵ0)=8.99×109 N⋅m2/C2 .

2) Two charged spheres separated by 2m are suspended vertically from a horizontal beam by insulating...

2) Two charged spheres separated by 2m are suspended vertically from a horizontal beam by insulating strings. The spheres have the same mass 4kg. The charges on the spheres are 2 ?C and -3 ?C. (a) Calculate the electric force between the charges. Give both magnitude and direction. (b) Determine the electric potential (Volts) at a point midway between the charges. (c) What direction are the electric field lines for each charge?

A solid and nonuniformly charged insulating sphere has two regions of interest as shown above. The...

A solid and nonuniformly charged insulating sphere has two regions of interest as shown above. The charge per unit volume depends on the distance from the center of the sphere, ρ(r) = Ar-2e-br for r ≤ a. The parameters are given as A = 4.20 pC/m, b = 2.90 m-1, and a = 0.370 m. (a) Determine the electric flux through a Gaussian sphere with a radius r = 0.560 m and centered about the solid insulating sphere as shown...

Two spheres have the same diameter and mass, but one is solid and the other one...

Two spheres have the same diameter and mass, but one is solid and the other one is hollow. Assuming homogeneous densities and putting the origin at the center, calculate the inertia tensor of each sphere.