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# Two 2.0 -g spheres are suspended by 10.0 -cm-long light strings (Fig. $\mathrm{P} 15.63 ) .$ A uni-form electric field is applied in the $x$ -direction. If the spheres have charges of $-5.0 \times 10^{-8} \mathrm{C}$ and $+5.0 \times 10^{-8} \mathrm{C}$ , determine the electric field intensity thatenables the spheres to be in equilibrium at $\theta=10^{\circ}$ .

## $4.4 \times 10^{5} \mathrm{N} / \mathrm{C}$

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### Video Transcript

the electric field were asked to find elected Feel that enables of these two charges, um, remain a typical beer making, um, 10 degrees here. I ran into equilibrium. We can find it by resolving the forces here. So this force will be so the Here's attention in the stream we presented by T. This will be the competent off attention, which is a t cost data. And downward will be the force of gravity, which is a call to the weight off the mask that is mg. And this will be ah minus t. Sign that up. And this will be the electric force to keep the charges in Korea. So force equilibrium. Ah, fortunately charge should be zero for the navy to charge or a negative charge. Maybe to charge charge, which is here. This is negative. Charge. This is positive charge. Um do you call? Stayed up physical. Two mg. Then attention will be here from here. Attention will be called mg divided by course. State up. We can write. The electric field force will be cool to cake you square divided by two l ah, sign. Better square. This is the distance between them from here to here. This is a distance which is to l sign that this is the l the length off the street plus t sign they don't. We will substitute their value for attention from this equation. This equation will substitute that owned by substituting that we get the question the impression that is it cule. Okay, Q squared, divided by two times l sign Better Square plus m g getting that so the costs and take a sign will change. Entertain that here. Then we'll solve for electric field here from this equation By solving for electric field, we get the question that is a que que que que tu l sign that square plus M g staying later. Divided by Q substituting values, we get the electric field to be 4.4 times 10 to the power of five Nugent for cool.

Wesleyan University