Fleming's left hand rule: Solved numerical

let's solve a couple of new miracles to get practice on Fleming's left hand rule so here's the first one a proton moving towards East enters a uniform magnetic field directed downwards find the direction of the force acting on it so first let's get our directions clear this is north this is south this is east this is west up down alright so up is outside the screen down is into the screen that's how we'll do it and to figure out the force we're going to use Fleming's left hand rule which basically says you stretch out these three fingers such that they are perpendicular to each other all of them mutually perpendicular to each other as you can see and then what do these fingers represent well I remember FBI thumb represents the force four finger represents F BB stands for magnetic field don't ask me why B but that's how it is so magnetic field FBI and this stands for current so we have to align our fingers accordingly and we'll get the direction of the force so great idea to first pause the video and see if you can try this yourself first all right let's do this a proton moving towards East proton is a positively charged particle so if it's moving towards the east then the current is also towards the east and so FBI this finger is pointing towards east enters a uniform magnetic field directed downwards FBI this is the magnetic field it's directed downwards so I have to point this finger down keeping this this way no not like that I'll rotate it like this there is now I'm just going to confirm current is to the east magnetic field is downwards perfect and so the direction of the force acting is the thumb and so the force is to the north all right let's do a second one an electron moving vertically upward is deflected towards the South by a uniform magnetic field find the direction of the magnetic field so in this case we are given the direction of the current in terms of electron we're also given in what direction the force is acting it's deflected towards South so the force acting on the electron is to the south we have to find the direction of the magnetic field so again great idea to pause the video and see if you can do this yourself right let's do this let's bring in our left hand and stretch it so an electron is moving vertically upwards now it's important is the electron is in negative charge so if a negative charge moves up the current is in the opposite direction so the current is actually downwards all right so that's the tricky part over here be careful with the electrons electrons are tricky so the current is downwards FBI middle finger has to point downwards okay and it's given it's deflected towards the south so the force is given to me force which is given bottom is deflect FBI so forces bottom is deflected towards the south that means force is this way downwards southwards force is to the south yeah that's how we more handle so let's just confirm current is downward yeah and the force is to the south and there it is this gives us the magnetic field FBI B for magnetic field the magnetic field is to the east now to be technically correct the magnetic field doesn't have to be towards the east although East is one of the right answers there are many answers over here why because we've seen in a previous video that when you're using Fleming's left hand rule une of the direction even if the angle between the magnetic field and the current is not 90 degrees even if they had some other nonzero angle the force direction would still be the same therefore in this example even if the magnetic field was not towards the east but maybe making some angle with the east in the downward direction the force on the electron would still be the same the electron would still have deflected towards the south so the magnetic field could be directed this way making some angle between East and the downward direction or it could be this way or it could be this way so strictly speaking to be technically correct the magnetic field can take any nonzero angle between the downward direction and the east direction any of them is fine but usually when you have questions like this we can still write we can always write the magnetic field must be towards in the east that is still a correct answer one of the correct answers so what did we learn in this video whenever we have to solve problems including magnetic forces acting on currents or moving charges just use your Fleming's left hand rule and remember FBI force magnetic field and current