The magnetic field at a distance ro from a long straight wir

The magnetic field at a distance r_o from a long straight wire carrying a current I is given by B=u₀I/2PI r_o . For the statements below, circle the word or phrase that correctly completes the sentence.

A) For a fixed current of 3.00 A in the wire, the magnetic field sensed by a Hall probe will _________________ if the distance r₀is changed from 0.6 cm to 1.2 cm. (double, triple, reduce to half, reduce by 0.6 mT)

B) If the current I is reduced from 3.00 A to 1.50 A for a fixed value of r₀= 2.00 cm, the magnetic field sensed by a Hall probe will_________________________. (double, triple, reduce to half, reduce by 1.5 mT)

C) If B is plotted against several values of r₀for a fixed current I, the graph will be a ______________________ . (straight line of positive slope, straight line of negative slope, curve decreasing with increasing r (positive curvature), curve increasing with increasing r (negative curvature)

D) Regions of constant magnetic field around a current carrying wire form _________________________ when viewed in cross section. (straight lines, triangles, circles, squares, hyperbolas)

E) If B is plotted against several values of I for a fixed distance r₀, the graph will be a _________________ . (straight line of positive slope, straight line of negative slope, curve upwards of positive curvature, curve downwards of negative curvature).

Solution

B = (uo*I)/(2**r)

(A)
Bnew =  (uo*I)/(2**(2*r)) = B/2
If we Double the Distance, B will become Half of the Original Value.
Correct Option = reduce to half

(B)
If Current is Halved, As Magnetic Field is directly proportional to Current, Manetic Field will also beocme Half,
Correct Option = reduce to half

(C)
The Curve will be similar to X = 1/Y , Bcoz that\'s how the relation is btw B & r.

Correct Option = Curve will be decreasing with increasing r (positive curvature).

(D)
It is allways Circles, around a Current Carrying Wire.
Correct Option - Circles.

(E)
B is directly proportional to I.
Curve will be similar to, X = Y
Correct Option = Straight line of positive slope