By which relation is the deflection of the coil θ related to the electrical current i in a moving coil galvanometer?

1. $i\propto \tan \theta$                 

2. $i\propto \theta$ 

3. $i\propto {\theta }^2$                    

4. $i\propto \sqrt{\theta }$ 

Three long, straight, and parallel wires carrying currents of 30 A, 10 A, and 20 A in P, Q, and R, respectively, are arranged as shown in the figure. What is the force experienced by a 10 cm length of wire Q?

When a positively charged particle moves in an x-y plane, its path abruptly changes due to the presence of electric and/or magnetic fields beyond P. The curved path is depicted in the x-y plane and is discovered to be noncircular. Which of the following combinations is true?
          
1. \(\overrightarrow{\mathrm{E}}=0 ; \overrightarrow{\mathrm{B}}=\mathrm{b} \hat{\mathrm{i}}+\mathrm{c} \widehat{\mathrm{k}}\) 
2. \(\overrightarrow{\mathrm{E}}=\mathrm{ai} ; \overrightarrow{\mathrm{B}}=\mathrm{c} \widehat{\mathrm{k}}+\mathrm{a} \hat{\mathrm{i}}\)
3. \(\vec{E}=0 ; \vec{B}=c \hat{j}+b \widehat{k}\)
4. \(\overrightarrow{\mathrm{E}}=\mathrm{ai} ; \overrightarrow{\mathrm{B}}=c \widehat{\mathrm{k}}+\mathrm{b} \hat{\mathrm{j}}\)

Two insulated rings, one of a slightly smaller diameter than the other, are suspended along their common diameter as shown. Initially, the planes of the rings are mutually perpendicular. What happens when a steady current is set up in each of them?

A charge Q is uniformly distributed on a ring of radius R made of an insulating material. If the ring rotates about the axis passing through its centre and normal to the plane of the ring with constant angular speed ω, then what will be the magnitude of the magnetic moment of the ring?

1. $Q\omega R^2$
2. $\frac{1}{2}Q\omega R^2$
3. $Q{\omega }^{2}R$
4. $\frac{1}{2}Q{\omega }^{2}R$

Two long parallel copper wires carry currents of 5 A each in opposite directions. If the wires are separated by a distance of 0.5 m, then the force between the two wires will be:

A long wire A carries a current of 10 A. Another long wire B, which is parallel to A and separated by 0.1 m from A, carries a current of 5 A, in the opposite direction to that in A. What is the magnitude and nature of the force experienced per unit length of B?
$({\mu }_0=4\mathrm{\pi }\times {10}^{-7}weber/amp-\mathrm{m})$
 

What is the relation between voltage sensitivity (σ_v) and current sensitivity (σ_i) of a moving coil galvanometer? (Resistance of Galvanometer = G)

1. $\frac{{\sigma }_i}{G}={\sigma }_v$                           

2. $\frac{{\sigma }_v}{G}={\sigma }_i$

3. $\frac{G}{{\sigma }_v}={\sigma }_i$                           

4. $\frac{G}{{\sigma }_i}={\sigma }_v$

A galvanometer having a coil resistance of \(60~\Omega\) shows full-scale deflection when a current of 1.0 A passes through it. How can we convert it into an ammeter capable of reading currents up to 5.0 A?

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns. What will the magnetic field be at the centre of this n-turn coil?