Two toroids \(1\) and \(2\) have total no. of turns \(200\) and \(100\) respectively with average radii \(40~\text{cm}\) and \(20~\text{cm}\) respectively. If they carry the same current \(i,\) what will be the ratio of the magnetic fields along the two loops?
1. \(1:1\)
2. \(4:1\)
3. \(2:1\)
4. \(1:2\)

A galvanometer has a resistance of 3663 $\Omega$. A shunt S is connected across it such that 1/34 of the total current passes through the galvanometer. The value of the shunt is :

(1) 3663 $\Omega$

(2) 111 $\Omega$

(3) 107.7 $\Omega$

(4) 3555.3 $\Omega$

A candidate connects a moving coil voltmeter \(V\), a moving coil ammeter \(A\), and a resistor \(R\) as shown in Fig. 6.58. If the voltmeter reads \(20~\text{V}\) and the ammeter reads \(4~\text{A}\), \(R\) is: 

1. equal to \(5~\Omega\)
2.  greater than \(5~\Omega\)
3.  less than \(5~\Omega\)
4. greater or less than \(5~\Omega\) depending upon its material.

A milliammeter of range 10 mA and resistance 9$\Omega$ is joined in a circuit as shown in Fig. 6.57. The meter gives full-scale deflection for current I when A and C are used as its terminals if current enter at A and leaves at C (B is left isolated). The value of I is :

(1)100 mA

(2) 900 mA

(3) 1 A

(4) 1.1 A

The endpoints of a current-carrying wire lie on the x-axis and y-axis as shown. The magnetic force on the wire is:

1. Zero

2. 6 N

3. 8 N

4. 10 N

The given figure shows a semicircular loop of radius R carrying current I and is placed in a uniform magnetic field B. The force acting on the semicircular part of the loop is

1. $B_0\pi lR$

2. $2\mathrm{\pi lRB}$

3. $lRB$

4. $2lRB$

A non-conducting rod AB of length L has a positive linear charge density $\lambda$. This rod is rotated about its one end with an angular speed $\omega$ as shown. The magnetic moment associated with this rod is-

1. λ$\frac{L^3\omega }{3}$

2. λ$\frac{L^3\omega }{6}$

3. $\frac{\pi L^3\omega }{12}$

4. $\frac{\pi L^3\omega }{24}$