A device called a toroid (figure) is often used to create an almost uniform magetic fiedl in some enclosed area. The device consists of a conducting wire wraped around a ring (a torus) made of a non conducting material. For a toroid having `N` closely spaced turns of wire, calculate the magnetic field in the region occupied by the torus, a distasnce `r` from the centre.

PQRS is a square region of side 2a in the plane of paper. A uniform magnetic field B, directed perpendicular to the plane of paper and into its plane is confined within this square region. A square loop of side 'a' and made of a conducting wire of resistance R is moved at a constant velocity vec(v) from left to right in the plane of paper as shown. Obviously, the square loop will enter the magnetic field at some time and then leave it after some time. During the motion of loop, whenever magnetic flux through it changes, emf will be induced resulting in induced current. Let the motion of the square loop be along x-axis and let us measure x coordinate of the centre of square loop from the centre of the square magnetic field region (taken as origin). Thus, x coordinate will be positive if the centre of square loop is to the right of the origin O (centre of magnetic field) and negative if centre is to the left. External force required to maintain constant velocity of the loop for x = -(9)/(5) a will be

PQRS is a square region of side 2a in the plane of paper. A uniform magnetic field B, directed perpendicular to the plane of paper and into its plane is confined within this square region. A square loop of side 'a' and made of a conducting wire of resistance R is moved at a constant velocity vec(v) from left to right in the plane of paper as shown. Obviously, the square loop will enter the magnetic field at some time and then leave it after some time. During the motion of loop, whenever magnetic flux through it changes, emf will be induced resulting in induced current. Let the motion of the square loop be along x-axis and let us measure x coordinate of the centre of square loop from the centre of the square magnetic field region (taken as origin). Thus, x coordinate will be positive if the centre of square loop is to the right of the origin O (centre of magnetic field) and negative if centre is to the left. External force required to maintain constant velocity of the loop for x = -(9)/(5) a will be

PQRS is a square region of side 2a in the plane of paper. A uniform magnetic field B, directed perpendicular to the plane of paper and into its plane is confined within this square region. A square loop of side 'a' and made of a conducting wire of resistance R is moved at a constant velocity vec(v) from left to right in the plane of paper as shown. Obviously, the square loop will enter the magnetic field at some time and then leave it after some time. During the motion of loop, whenever magnetic flux through it changes, emf will be induced resulting in induced current. Let the motion of the square loop be along x-axis and let us measure x coordinate of the centre of square loop from the centre of the square magnetic field region (taken as origin). Thus, x coordinate will be positive if the centre of square loop is to the right of the origin O (centre of magnetic field) and negative if centre is to the left. For x = a//4 (i) magnetic flux through the loop, (ii) induced current in the loop and (iii) external force required to maintain constant velocity of the loop, will be

PQRS is a square region of side 2a in the plane of paper. A uniform magnetic field B, directed perpendicular to the plane of paper and into its plane is confined within this square region. A square loop of side 'a' and made of a conducting wire of resistance R is moved at a constant velocity vec(v) from left to right in the plane of paper as shown. Obviously, the square loop will enter the magnetic field at some time and then leave it after some time. During the motion of loop, whenever magnetic flux through it changes, emf will be induced resulting in induced current. Let the motion of the square loop be along x-axis and let us measure x coordinate of the centre of square loop from the centre of the square magnetic field region (taken as origin). Thus, x coordinate will be positive if the centre of square loop is to the right of the origin O (centre of magnetic field) and negative if centre is to the left. For x = a//4 (i) magnetic flux through the loop, (ii) induced current in the loop and (iii) external force required to maintain constant velocity of the loop, will be

PQRS is a square region of side 2a in the plane of paper. A uniform magnetic field B, directed perpendicular to the plane of paper and into its plane is confined within this square region. A square loop of side 'a' and made of a conducting wire of resistance R is moved at a constant velocity vec(v) from left to right in the plane of paper as shown. Obviously, the square loop will enter the magnetic field at some time and then leave it after some time. During the motion of loop, whenever magnetic flux through it changes, emf will be induced resulting in induced current. Let the motion of the square loop be along x-axis and let us measure x coordinate of the centre of square loop from the centre of the square magnetic field region (taken as origin). Thus, x coordinate will be positive if the centre of square loop is to the right of the origin O (centre of magnetic field) and negative if centre is to the left. For x = -9a//5 , magnitude of induced current and its direction as seen from above will be:

PQRS is a square region of side 2a in the plane of paper. A uniform magnetic field B, directed perpendicular to the plane of paper and into its plane is confined within this square region. A square loop of side 'a' and made of a conducting wire of resistance R is moved at a constant velocity vec(v) from left to right in the plane of paper as shown. Obviously, the square loop will enter the magnetic field at some time and then leave it after some time. During the motion of loop, whenever magnetic flux through it changes, emf will be induced resulting in induced current. Let the motion of the square loop be along x-axis and let us measure x coordinate of the centre of square loop from the centre of the square magnetic field region (taken as origin). Thus, x coordinate will be positive if the centre of square loop is to the right of the origin O (centre of magnetic field) and negative if centre is to the left. For x = -9a//5 , magnitude of induced current and its direction as seen from above will be: