Electric Field of the Earth. The earth has a net electric charge that causes a field at points near its surface equal to 150 N/C and directed in toward the center of the earth. (a) What magnitude and sign of charge would a 60-kg human have to acquire to overcome his or her weight by the force exerted by the earth's electric field?

Video transcript

Hi, everyone. In this particular problem, we are asked to actually find the method and the sign of charge that will make the sphere suspended in the air where we have a metallic sphere of charge Q which is being asked and mass one kg released from rest from rest at a high d above a large plate where we will have an electric field due to its plate at approximately 1 15 new temper Coolum and points towards the plate. So first, what we want to do is to actually identify and make the free body diagram of the metallic sphere. So we will have a metallic sphere here where we will then also have obviously the gravitational forces or the weight, which is just MG. And at the same time, we are asked to find the electric field that will counter that, that will make the sphere suspended in the air or floating. So what? And we are also asked to find what the magnitude and the sign of the charge. So M G here is the gravitational force and it is directed downward and F is the electric static electrostatic force which F will equals two Q times E which is Q, it's just going to be the charge, absolute value of the charge and E is going to be the electric field. Okay. So we're asked to find that the sphere is suspended. So when the sphere is suspended in the air, then we will have to actually satisfy this equation. So for the sphere to be suspended, the F and the M G has to be equal. So F plus MG will have to be equal to zero because essentially it will have no acceleration and to stay suspended in the air, the sum of all forces applied should be zero. So to balance the weight of the sphere itself, to balance the gravitational force, the electric force must be upward, the electric field is downward. So for an outward force, the charge Q of the sphere must be negative because negative charges experience a force directed against the electric field. So we know that we have an electric field due to the plate, the plate is going to be like here. So we will have an electric field due to the plate which is pointing downward. So for an upward force, which is the one that we want here, the charge Q of the sphere must be negative because negative charges, experience of force directed against the electric field, we want to remember that. So I'm just gonna write down Q or sphere charge has to be negative because then because Nick church experience a force. So this is the electric field force and the force directed against. Yeah, just like that. Okay. So then we can start by, we can start actually finding the magnitude of the charge by just using this formula right here. So we want this to force us to be equal. So we want to have Q mhm close uh equals mg just like so or essentially, you can also do Q E we thought the absolute value here if we do not know what this site is lies what this logic is plus entry equals to zero just like that. And then solve and then the Q will turn out to be a minus, we're using this. But because we know that the sphere charge has to be negative, we can just equal this together because we know that it has to be um equal forces. So with this, we are rearranging. So the key, the Q will then be MG over E and the M is given to be one kg, The mass of the sphere, the G is just the normal 9.81 m/s squared. and E is also given which is 150 Newton per And this really calls to be 6.5, 4 times 10 to the power of -2 cool. Um and that is just the absolute value of the charge the magnitude. So, so charge Q Is then going to be -6.54 then stand to the part of minus to cool them just like that. And that answer will actually respond to option A just like so and that will be all for this particular practice problem. And if you guys have any sort of confusion on this particular topic, please make sure to check out our other lesson videos and it will be all for this video. Thank you.