# Magnetic field calculation

by denian
Tags: calculation, field, magnetic
 P: 1,786 Magnetic field calculation Denian, you need to figure out which component of the earth's magnetic field, say H, adds to the magnetic field of the solenoid (given by $$B_{solenoid} = \mu_{0}nI$$ where n is the no of turns per unit length and I is the current carried by it). The component would be of the form $$H cos\theta$$ or $$H sin\theta$$ depending on how you measure theta. The best way to go about it is to draw a diagram showing the two vectors B and H due to the solenoid and the earth at a point (remember that B is axial and will be strongest inside the solenoid--the above expression is that approximated for a closed pack coil). Then, you should realize that if the needle comes into equilibrium 37 west of north (or whatever you're given in a general case), the net force on the needle is zero (for if it were not zero, there could have been a torque that could cause further deflection..but its static so reversing this logic, I can say that the NET force on it at this point in time is zero). Use the equation for the force/torque. BUT: You need to understand that this whole solenoid+earth system can be replaced (in effect) by a net field $$B_{net}$$ which is the vector sum of the fields of the solenoid (axial, direction given by Right Hand Rule or Fleming rule whatever you wish to use) and that of the earth (I call the earth's field H). The earth's field has a horizontal component and a vertical component. Resolve it using the angle of dip/declination. If you are having trouble doing this, the sites I have given in my previous post should help. Finally if you just can't get things to work, send your complete solution and I'll try to see what the problem is. There is no big deal here, its just the directions you and I have to take care of and the rest is mincemeat math. Cheers Vivek EDIT: Give me a few hours denian, while you follow the advice given in this post and I'll figure out the equations myself and give you the answer.
 P: 1,786 Hi denian The vector diagram is okay. If you used it to write, $$B_{resultant} = \sqrt{B_{earth}^{2} + B_{solenoid}^2}$$ then all your subsequent computions should be okay too (as they are indeed as you get the correct answer). Do you still have doubts about your working? Cheers Vivek