The current in Fig. E29.18 obeys the equation I(t) = I_0e^(-bt), where b > 0.

Find the direction (clockwise or counterclockwise) of the current induced in the round coil for t > 0.

Video transcript

Hey, everyone. So this problem is dealing with induced current. Let's see what it's asking us in the assembly of conductors shown where we have a metallic ring sitting to the left of a straight wire conductor where we have an induced current moving in the negative Y direction. If the page is kind of an X Y plane, we're asked to determine whether the current induced in the ring is clockwise or anticlockwise. If the current in the straight wire is given by the equation I of T equals I knot multiplied by E to the negative K T where both K and T are positive. Our multiple choice answers are a counterclockwise B clockwise C no current induced or D, none of these. So the first thing we can do here is recognize that in the equation for current, if both K and T are positive, we're going to have E to the negative value. So we know that are E to the negative X, we can recall that graph of something like this where as time increases or our um value continually decreases. So we know that our current is continually decreasing. We can then use our right hand rule to find the direction of the magnetic field. So we take our pointer finger move that in the direction of the of the current. Our middle finger is the magnetic field lines, the pointing away from the ring. And then our thumb is the magnetic field direction, which is out of the page. We can recall lenses law which tells us that the field of the induced current is in the opposite direction of the magnetic field. So the field for the induced current is going to be into the page. And then we can lastly use our right hand brick rule where our thumb goes in the direction of the field of induced current and our fingers curled in the direction of the flow of the current. So our right hand rule, thumb goes into the page, our fingers curl in a clockwise direction. And so that is the answer to this problem. We'll have a clockwise flow of current. All right, that's all we have for this one. We'll see you in the next video.