In the circuit shown below, a current 3I enters at A. The semicircular parts ABC and ADC have equal radii ‘r’ but resistances 2R and R respectively. The magnetic field at the center of the circular loop ABCD is ___________.

Fill in the blank with the correct answer from the options given below.

A circular coil of 50 turns and radius 10 cm carrying a current of 5.0 A is suspendedvertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field linesmake an angle of 90° with the normal of the coil. Calculate the magnitude of thecounter torque that must be applied to prevent the coil from turning?

Which of the following is the correct expression for cyclotron frequency?

A uniform magnetic field of 2 T exists in a cylindrical region of radius 10 cm, itsdirection parallel to the axis along east to west. A wire carrying current 6 A in the northto south direction passes through the region. What is the magnitude of the force onthe wire if

(a) the wire intersects the axis

(b) the wire in the N-S direction is lowered from the axis by a distance of 6 cm?

A galvanometer coil has resistance 20 Ω and the metre shows full scale deflectionfor a current of 2 mA. How will you convert the metre into an ammeter of range 0 to6 A?

​Consider a solenoid of 5.0 cm length and radius 0.40 cm. It consists of 500 turns of wire and carries a current of 3.0 A. The magnitude of magnetic field at the centre of the solenoid is close to [($$\frac{μ_o}{4π})=10^{-7}$$​ Tm/A]:​

A current element of length 0.8 cm carrying a current of 5 A towards +x- direction is placed symmetrically at the origin along the x-axis. The magnetic field at a point (0, 5 cm) is:

(i, j and k are unit vectors along the x-axis, y-axis and z-axis, respectively.)

A 3.0 cm segment of a wire, centred at the origin (0, 0, 0) lies along Y-axis. It carries a current of 6.0 A in positive Y-direction. The magnetic field due to this segment at a point (3.0 m, 0, 0) is [$$(\frac{μ _o}{4π})=10^{-7}$$​ Tm/A, and i, j and k are unit vectors along X-axis, Y-axis and Z-axis, respectively]

A coil is carrying a current of 10 A and has radius 10 cm and number of turns 500. It is rewound to make a new coil of radius 5 cm and it carries same current 10 A. The ratio of magnetic moment of original coil to that of new coil is

A 2.0 m long metallic rod is rotated with an angular frequency of 100 rad/s about an axis normal to the rod and passing through its one end. A uniform magnetic field of 2.0 T exits parallel to the axis. The emf induced between the two ends of the rod is:

Consider an ideal toroid of average radius 16.0 cm with 240 turns. A current of 10 A is maintained in it. The magnitude of magnetic field inside the toroid is [$$(\frac{μ_0}{4π})=10^{-7}$$​ Tm/A]: