Two long straight wires are oriented perpendicular to the co

Two long, straight wires are oriented perpendicular to the computer screen, as shown in the figure, in which L = 4.0 cm. The current in one wire is I1 = 3.4 A, pointing into the screen, and the current in the other wire is I2 = 4.0 A, pointing out of the screen. Find the magnitude and direction of the net magnetic field at point P.

_____ T

_____° (clockwise from the dashed line to the right of P)

Solution

We know that the magnetic field due to long wires is given as: B = _oI / 2R where I is the current and R is the distance from the wire.

Also the direction of the magnetic field can be obtained by curling our right around the wire with the thumb pointing towards the current, then the curl of the fingers give the direction of the magnetic field.

Now for the wire L1 the magnetic field would be towards right, while for the wire L2, the field would be towards the left but inclined with the horizontal such that it is perpendicular to the line joining P to the L2.

Net magnetic field along the horizontal would be: _oI₁ / 2L - _oI₂ Cos45/ 2L2 = (_o / 2L)[I₁ - I₂/2]

Bx = (2 x 10^-7/0.04)[3.4 - 4/2] = 70 x 10^-7 T so the net magnetic field along the horizontal would be towards the right.

Net magnetic field along the vertical would be due to the vertical component of the field generated by I2,

So we have: By = -_oI₂ Sin45/ 2L2 = 2 x 10^-7 x 4 /0.04 x 2 = -100 x 10^-7 T; the minus sign denotes that the magnetic field would be directed downwards.

Therefore the net magnetic field would be: 122.066 x 10^-7 T = 12.207 T

For the angle with the horizontal, say , we can write: tan = 100/70

or, = 55.0 degrees

Therefore the required angle is 55 degrees