Question

A horizontal compass is placed 21 cm due south from a straight vertical wire carrying a 35 A current downward. In what direction does the compass needle point at this location? Assume the horizontal component of the Earth's field at this point is 0.45 ✕ 10^-4 T and the magnetic declination is 0°. Calculate degree and specify direction.

Answer 1

Data given, Distancefrom wire,r -21cm Current/ 35 A Magneticfield of earth, B,0.45x104T Magnetic declination is the deviation of the magnetic north (the direction the north end ofa compass needle points) from the geographic north pole of the earth (the true north) The needle of a compass always lies along the magnetic field lines of the earth. If the magnetic declination at a point on the earth's surface is zero, it means that the horizontal component of the earth's magnetic field line at that point lies along the line of the north-south magnetic poles Now, the presence of a current carrying straight vertical wire creates an additional magnetic field that must be combined with the earth's magnetic field. Since magnetic fields are vectors, the magnetic field of the earth and the magnetic field of the vertical wire must be combined vectorally The net magnetic field is 4rx10 Tm/A (35A) 27(21x102m -0.333 104T Calculate the direction 1ath tan . | 0.333x10"T 53.74° Hence, the compass needle points along the direction of53.74° west of north