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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

Honeybees acquire a charge while flying due to friction with the air. A 100mgbee with a charge of +23pCexperiences an electric force in the earth’s electric field, which is typically 100N/C, directed downward.

a. What is the ratio of the electric force on the bee to the bee’s weight?

b. What electric field strength and direction would allow the bee to hang suspended in the air?

The surface charge density on an infinite charged plane is -2.0×10-6C/m2 . A proton is shot straight away from the plane at 2.0×106m/s. How far does the proton travel before reaching its turning point?

You have a summer intern position with a company that designs and builds nanomachines. An engineer with the company is designing a microscopic oscillator to help keep time, and you’ve been assigned to help him analyze the design. He wants to place a negative charge at the center of a very small, positively charged metal ring. His claim is that the negative charge will undergo simple harmonic motion at a frequency determined by the amount of charge on the ring.

a. Consider a negative charge near the center of a positively charged ring centered on the z-axis. Show that there is a restoring force on the charge if it moves along the z-axisbut stays close to the center of the ring. That is, show there’s a force that tries to keep the charge at z=0. b. Show that for small oscillations, with amplitude <<R, a particle of mass mwith charge-qundergoes simple harmonic motion with frequency f=12πqQ4πε0mR3,RandQare the radius and charge of the ring.

c. Evaluate the oscillation frequency for an electron at the center of a 2.0μmdiameter ring charged to 1.0×10-13C.

The irregularly shaped area of charge in FIGURE Q23.7 has surface charge densityηi. Each dimension (x and y) of the area is reduced by a factor of 3.163.

a. What is the ratio ηf/ηi , where ηfis the final surface charge density?

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Two 2.0-cmdiameter disks face each other, 1.0mmapart. They are charged to ±10nC.

a. What is the electric field strength between the disks?

b. A proton is shot from the negative disk toward the positive disk. What launch speed must the proton have to just barely reach the positive disk?

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