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# A small plastic ball of mass $m=2.00 \mathrm{g}$ is suspended by a string of length $L=20.0 \mathrm{cm}$ in a uniform electric field, as shown in Figure $\mathrm{P} 15.52$ . If the ball is in equilibrium when the string makes a $\theta=15.0^{\circ}$ angle with the vertical as indicated,what is the net charge on the ball?

## $q=5.25 \mu \mathrm{C}$

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### Video Transcript

so here in this problem we have to calculate the net charge on the ball. Onda were given that the moss off the ball is to Graham so we can take it as 0.2 kg Onda, the length off the string were given us 20 centimeters. That means 0.0 Sorry, It 0.2 m on this angle theater were given us 15 degree so there's a free body diagram. Now we're going to balance the force in the vertical direction that is Sigma. If we should be equal to zero because the ball is in equilibrium So they can say that Geico Santita will be called toe MGI. So from her t will be called toe MGI over Hussein Tito the next heavily balancing the force in the horizontal direction. So we have t scientific data. Is it called toe Effie? We can pluck the value of tea here so we'll get electric force f e s. This is mg over Jacinta times scientists. So it becomes changing data. So this is F E. Now we know that f e is equals toa que in tow e where he is electric field strength on cue Wisdom Charge on the net charge on the ball. So from here, the net charge on the balk You will be called Tau e over e. So if we have mgt Agent theater divide by E as it is now, we can plug all the values here to calculate electric charge on the ball. So you want to plug all the valleys here So mass we have zero point 002 kg times g. We have 9.81 m per second squared times change In theater, we have 10 attention 15 degree divide by electric field strength on the electric field. Strength is one times 10 to the power three Newton over column. So from here we'll get the value as 5.25 times 10 to the power minus six column. Or if ride the answer in micro column will get 5.25 Micro column So this is the net charge on the ball. So I hope you have understood the problem. Thank you

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