The figure shows a long wire bent in the middle to form a right angle. Show that the magnitudes of the magnetic fields at the points $Q$ and $R$ are unequal and find these magnitudes. The wire $w_1$ and the circumference of a circle are coplanar and $w_2$ is perpendicular to the plane of the paper. Also, find the ratio of the field at $Q$ and $R$, 

A long wire carrying a current $i$ is bent to form a plane angle $\theta$. Find the magnetic field $B$ at a point on the bisector of this angle situated at a distance $x$ from the vertex is written in the form of $K\cot \frac{\theta }{4} \mathrm{T}$. Then, find the value of $K$.

(i) Two circular coils of radii $5.0 \mathrm{cm}$ and $10 \mathrm{cm}$ carry equal currents of $1 \mathrm{A}$. The coils have $50$ and $100$ turns respectively and are placed in such a way that their planes, as well as the centre, coincide. Find the magnitude of the magnetic field $B$ at the common center when the currents in the coils are (a) in the same sense (b) in the opposite sense. (ii) If the outer coil of the above problem is rotated through $90°$ about a diameter, what would be the magnitude of the magnetic field $B$ at the centre?

Two circular coils of wire each having a radius of $4 \mathrm{cm}$ and $10$ turns have a common axis and are $6 \mathrm{cm}$ apart. If a current of $1 \mathrm{A}$ passes through each coil in the opposite direction find the magnetic induction.

(a) At the centre of each coil

(b) At a point on the axis, midway between them.

Two wire loops $\mathrm{PQRSP}$ formed by joining two semicircular wires of radii $R_1$ and $R_2$ carries a current $I$ as shown in (figure). The magnitude of the magnetic induction at the center $\mathrm{C}$ is 

Find the magnitude of the magnetic induction $B$ of a magnetic field generated by a system of thin conductors (along which a current $i$ is flowing) at a point $\mathrm{A} (0, \mathrm{R}, 0)$, that is the centre of a circular conductor of radius $R$. The circular part is in $yz$ plane.

Find the magnetic induction of the field at the point $O$ of a loop with current $I$, whose shape is illustrated in figure

 (a) In figure $a$, the radii $a$ and $b$ as well as the angle $\varphi$ are known,

(b) In figure $b$, the radius $a$ and the side $b$ are known.

(c) A current $I=5.0 \mathrm{A}$ flows along a thin wire shaped as shown in the figure. The radius of a curved part of the wire is equal to $R=120 \mathrm{mm},$ the angle $2\varphi =90°$. Find the magnetic induction of the field at the point $O$.

Find the magnetic induction at the point $O$ if the wire carrying a current $I$ has the shape shown in figure $a, b, c$. The radius of the curved part of the wire is $R$, the linear parts of the wire are very long.