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Two2.0cmdiameter insulating spheres have a6.0cmspace between them. One sphere is charged to+10nC, the other to-15nC. What is the electric field strength at the midpoint between the two spheres?

Short Answer

Expert verified

The electric field strength at the midpoint| between the two spheres is5.56×105N/C.

Step by step solution

01

Formula for electric field intensity

The intensity of the electric field at a point dunits away from a point charge qcan be calculated using the following formula:

(E)=q/4πεd2NC-1

The vector sum of the intensities produced by the individual charges equals the intensity of the electric field at any point due to a number of charges.

02

Calculation for electric field at the midpoint| between the two spheres 

Distance between the outer edges is 6.7cm.

Diameter of sphere is2.0cm.

Hence the distance between center is(6.7+2.0)=8.7cm.

Mid point is ,

=(8.7/2)cm

localid="1648629844607" =4.35cm=0.0435m.

Charge of spherelocalid="1648629881080" 1islocalid="1648391289846" 41nC.

Charge of spherelocalid="1648629893533" 2is-76nC.

The fields will now all point in the same direction.

As a result, whole field is:

localid="1648630029365" Enet=E1+E2

localid="1648630472057" E1due tolocalid="1648630003851" 42nCwill be:

localid="1648630478720" E1=9×109×41×10-9(0.0435)2

localid="1648630485528" E1=1.95×105N/C

localid="1648630491962" E2due to localid="1648630497375" -76nCwill be:

localid="1648630504401" E2=9×109×76×10-9(0.0435)2

localid="1648630510652" E2=3.61×105N/C

03

Calculation for electric field strength at the midpoint| between the two spheres 

SubstituteE1andE2values we get,

Enet=E1+E2

Enet=1.95×105N/C+3.61×105N/C

Enet=5.56×105N/C

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Most popular questions from this chapter

A small segment of wire in FIGURE Q23.4contains 10nCof charge.

a. The segment is shrunk to one-third of its original length. What is the ratio of λf/λi, where λiandλf are the initial and final linear charge densities?

b. A proton is very far from the wire. What is the ratio Ff /Fi of the electric force on the proton after the segment is shrunk to the force before the segment was shrunk?

c. Suppose the original segment of wire is stretched to 10 times its original length. How much charge must be added to the wire to keep the linear charge density unchanged?

A sphere of radius R has charge Q. The electric field strength at distancer>RisEi. What is the ratio Ef/Eiof the final to initial electric field strengths if

(a) Q is halved,

(b) R is halved, and

(c) r is halved (but is still>R)? Each part changes only one quantity; the other quantities have their initial values

Air "breaks down" when the electric field strength reaches 3.0×106N/c, causing a spark. A parallel-plate capacitor is made from two 4.0cm×4.0cm electrodes. How many electrons must be transferred from one electrode to the other to create a spark between the electrodes?

An electron in a vacuum chamber is fired with a speed of 8300km/stoward a large, uniformly charged plate 75cm away. The electron reaches a closest distance of 15cm before being repelled. What is the plate’s surface charge density?

An electric dipole is formed from two charges, ±q, spaced1.0cm apart. The dipole is at the origin, oriented along the y-axis. The electric field strength at the point x,y=(0cm,10cm)is 360N/C.

a. What is the charge q? Give your answer in nC.

b. What is the electric field strength at the pointx,y=10cm,0cm?

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