Four long, straight wires, each carrying a current of 5.0 A, are placed in a plane as shown in figure . The points of intersection form a square of side 5.0 cm. (a) Find the magnetic field at the centre P of the square. (b) `Q_1, Q_2, Q_3 and Q_4` are points situated on the diagonals of the square and at a distance from P that is equal to the length of the diagonal of the square. Find the magnetic fields at these points. `

Explanation

Magnetic field at P due to wire `W_1` and `W_2` = 0 Magnetic field at P due to wires `W_3` and `W_4` = 0 Hence net magnetic field at P due to these four wires = 0 (b) At point `Q_1` Magneticfield due to `W_1 = 4xx10^(-5) T` along? Magnetic field due to ` W_2 = (4)/(3) xx10^(-5) T` along? Magneticj field due to `W_3 = 4xx10^(-5)T`along? Magnetic field due to `W_4 = (4)/(3)xx10^(-5) T` along? So net B at `Q_1 = ((4+(4)/(3) + 4 +(4)/(3))xx10^(-5)T` `=(32)/(3) xx106(-5)T` `=1.06xx10^(-4)T` along 3 At point `Q_2` Magnetic field due to wire `W_1 = 4xx10^(-5) T` along ox` Magnetic field due to wire `W_2 = (4)/(3) xx10^(-5) T along ox` Magnetic field due to wire `W_3 = (4)/(3) xx10^(-5)T along ox` Magnetic field due to wire `W_4 = 4xx10^(-5)T along ox` `
` Hence net B = 0 Similarly at point `Q_3` and `Q_4` magnetic field be 1.1xx10^(-4)T along `ox` and zero.