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# A small sphere of charge $q=+68 \mu \mathrm{C}$ and mass $m=5.8 \mathrm{g}$ is attached to a light string and placed in a uniform electric field $\overrightarrow{\mathrm{E}}$ that makes an angle $\theta=37^{\circ}$ with the horizontal. The opposite end of the string is attached to a wall and the sphere is in static equilibrium when the string is horizontal as in Figure $\mathrm{P} 15.22$ . (a) Construct a free body diagram for the sphere. Find (b) the magnitucle of the electric field and (c) the ten-sion in the string.

## a. $1.4 \times 10^{3} N / C$b. $1.4 \times 10^{3} \mathrm{N} / \mathrm{C}$ c. $7.5 \times 10^{-2} N$

### Discussion

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##### Christina K.

Rutgers, The State University of New Jersey

##### Jared E.

University of Winnipeg

### Video Transcript

headers to grant slash Start our discussion. Electric fit. That's now Suppose you have a fair off Char's you and that is 68 Micro Coolum not and the mass off US fair is five point Edra, not this fair is tied with a string. This is a string and this is some hearts harsh office. Not this fair is experiencing an electric field on this side and the angle between from Holy Gentle is 37 degrees. No. First we have to construct a free body diagram for this fair. Let's see, how can we do that? So suppose if this is a spare and it had some masked men, it will experience of force in downward direction. That is mg. Okay, hang. If Electric Field is in this direction, then there is there must be an electric fourth also in this direction. So, uh, force in this direction, it means that half sine theta isn't ah, four direction and F course Tita is in this direction where two ties 37 degrees and also attention will generate in this direction on district. This is a free body diagram for this square. No, you have to find out the magnitude of the electric field. Let us see how we can find her. Basically, this MGI is balanced by this half sign Peter. So it will comes to be have signed Tita. Is it closed toe MGI and this Afghan Britain s Q E scientist er by a seacoast o m g So even comes out from here MGI by Hussein titter off Report the values that is 5.8 in tow Tenderness part ministry Cagey in tow 9.8 meters per second squared by 68 in tow 10 this par minus six Coolum into sign 37 the green Then if you solve this, you will get the value off is 1388.9 New temple Cool. No letters supposed you have to find Are the tension on the string that istea So this tension is balance out with half course Tater So that will be vehicles toe after ghostwriter So it will be your ego straighter now, by putting the values that is 68 in 10 minutes by minus six Coolum into 1388.9 u Turn Pakula electrical That is in tow. Course 37 degree you will get the value off 0.75 Neuter. This is the tension on the string. Well, this is all from me for this video. I hope you will like the video. Thank you.

Other Schools
##### Christina K.

Rutgers, The State University of New Jersey

##### Jared E.

University of Winnipeg