Question

Find the flux density B when the potential is given by x i + y j + z k in air.

(a) 12π x 10^-7

(b) -12π x 10^-7

(c) 6π x 10^-7

(d) -6π x 10^-7

I got this question in homework.

My doubt stems from Magnetic Vector Potential in portion Magnetostics of Electromagnetic Theory

Answer 1

The correct option is (b) -12π x 10^-7

For explanation I would say: The field intensity H = -Grad(V). Since the given potential is a position vector, the gradient will be 3 and H = -3. Thus the flux density B = μH = 4π x 10^-7 x (-3) = -12π x 10^-7 units.