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Integrated Concepts A 5.00 g charged insulating ball hangs on a 30.0 $\mathrm{cm}$ long string in a uniform horizontal electric field as shown in Figure 18.56 . Given the charge on the ball is $1.00 \mu \mathrm{C},$ find thestrength of the field.

$E=6900 \frac{\mathrm{N}}{\mathrm{C}}$

Physics 102 Electricity and Magnetism

Chapter 18

Electric Charge and Electric Field

Rutgers, The State University of New Jersey

Simon Fraser University

Hope College

Lectures

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Let's draw the diagram for this question. First, this is the vertical access. Andi. This is a string off length, 30 centimeters on. This is a insulating material ball on the lens off a string is so distant emitters that means it's 0.3 meters. Now we know that there is a word vertically down. We're acting forced off mg, which is a weight off the ball. There is electric field, horizontal to the horizontally to the right, and weight off the ball on dhe electric field have achieved equilibrium such that the boy, the string actually makes an angle off eight degrees. So let's find out. The tension in this drink says String has attention directed upwards, which is t on. Dhe ti has two components, one acting against MG, which creates the ball vertically in a vertical equilibrium on one, acting in opposite direction to eat, which creates the horizontal equilibrium. So let's find out this s t off course. I in theater, which is a dick, please, and this component here it's tension times sign off it decrease. So let's use this Equality t co sign off eight degrees is equal to mg. So from this weekend fine intention. So attention equals M. Times J divided by sign off, a decree so kosher enough it degrees no second equilibrium. Miss Teen signed. Eight Degrees equals charge Times Electric Field, which is a electric foot, which is electric force. We know that attention is MG, divided by co sign eight degrees. So we are asked to find electrics field strength, which is this? So if you substitute the value of tea from a question one inside this, you'd find MG. Turn eight degrees is equal to cure times E. Let's perform the calculation now. Electric field strength Ebba is given by mm. So let's substitute for values as well. 0.5 times gravity, which is 9.8 times. Turn off a dick tease divided by one micro Coolum, which is 10 power negative. Six cooler. If you perform this calculation, you will get the value 6886 Newton. We're cool. Um, but we want to keep only two significant digits. I'm sorry. We can keep three significant digits. So in this case, does it answer? It's 6890 Newton. Well, Cologne

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