Answer to Question #217566 in Electricity and Magnetism for Tia

Question

The force on differential length dl at point P in the conducting circular loop in
Figure 8.33 is
(a) Outward along OP
(b) Inward along OP
(c) In the direction of the magnetic field
(d) Tangential to the loop at P

Answer 1

(a) out ward along OP

$F=i(dl\times B)=idlBsin\theta$

$\theta=90°\\F=idlBsin90°$ =$idlB$

Outward along OP correct option

(b)

Inward along the OP

$$F=idlBsin\theta=idlBsin0°=0N$$

Incorrect option

Option (c)

Maximum value

Bio sawart law

$B=\frac{\mu_0 }{4\pi}\frac{I dlsin\theta}{r^2}$

Where $\theta=90°$

$B=\frac{\mu_0}{4\pi}\frac{I dl}{r^2}$

$dl=2\pi r$

Put value

$B=\frac{\mu_0}{4\pi}\frac{I 2\pi r}{r^2}$

$B_{o}=\frac{\mu_0l}{2\pi r}$ $\bigotimes$

Direction of magnetic field into the loop tangent of the loop $\theta=90°$

Magnetic field perpendicular to the distance.

Option (c) and (d) is incorrect option