A semi-circular arc of radius r and a straigh | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The magnetic field $B$ produced by the semi-circular arc at its center is given by $B = \frac{\mu_{0} i}{4 r}$.The direction of this magnetic fiel

Vedclass · Accepted Answer

$\left(\frac{\mu_{0} i^{2}}{4 r}\right)$

Vedclass · Answer

(A) The magnetic field $B$ produced by the semi-circular arc at its center is given by $B = \frac{\mu_{0} i}{4 r}$.The direction of this magnetic field is perpendicular to the plane of the arc (using the right-hand rule).The straight wire carrying current $i$ is placed along the diameter. The small element $P$ at the center of the diameter is in this magnetic field $B$.The magnetic force $dF$ on a small element of length $dl$ carrying current $i$ is given by $dF = i(dl 	imes B)$.Since the magnetic field $B$ is perpendicular to the wire,the magnitude of the force per unit length is $f = \frac{dF}{dl} = iB$.Substituting the value of $B$,we get $f = i \left(\frac{\mu_{0} i}{4 r}ight) = \frac{\mu_{0} i^{2}}{4 r}$.

$A$ semi-circular arc of radius $r$ and a straight wire along the diameter,both are carrying the same current $i$. Find out the magnetic force per unit length on the small element $P$,which is at the center of the diameter.

Similar Questions

What is the convention for an electric or magnetic field emerging out of the plane of the paper and going into the plane of the paper?

In the following figure,a wire bent in the form of a regular polygon of $n$ sides is inscribed in a circle of radius $a$. The net magnetic field at the centre will be

An infinitely long straight conductor is bent into the shape as shown below. It carries a current of $I$ ampere and the radius of the circular loop is $R$ metre. Then, the magnitude of magnetic induction at the centre of the circular loop is

Two parallel conducting wires of equal length are placed distance $d$ apart and carry currents $I_1$ and $I_2$ respectively in opposite directions. The resultant magnetic field at the midpoint of the distance between both the wires is

Two identical wires, carrying equal currents are bent into circular coils $A$ and $B$ with $2$ and $3$ turns respectively. The ratio of the magnetic fields at the centres of the coils $A$ and $B$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module