JEE Advanced Mi...

In front of an earthed conductor a point charge + q is placed as shown in figure :

In the figure shown the key is switched on at t = 0. Let I₁ and I₂ be the currents through inductors having self inductances L₁ & L₂ at any time t respectively. The magnetic energy stored in the inductors 1 and 2 be U₁ and U₂. Then  at any instant of time is :

Statement – 1 Four point charges q₁, q₂, q₃ and q₄ are as shown in figure. The flux over the shown Gaussian surface depends only on charges q₁ and q₂.

Statement – 2 Electric field at all points on Gaussian surface depends only on charges q₁ and q₂.

Statement 1 : A direct uniformly distributed current flows through a solid long metallic cylinder along its length. It produces magnetic field only outside the cylinder .

Statement 2 : A thin long cylindrical tube carrying uniformly distributed current along its length does not produce a magnetic field inside it. Moreover, a solid cylinder can be supposed to be made up of many thin cylindrical tubes.

Statement–1 : Magnitude of potential difference across the terminals of a non-ideal battery in a circuit cannot be greater than its emf.

Statement–2 : When a current of magnitude I is passing through a battery of emf E and internal resistance r as shown, the magnitude of potential difference (V) across the battery is given by V = E– I r

Statement–1 : No electric current will be present within a region having uniform and constant magnetic field.

Statement–2 : Within a region of uniform and constant magnetic field the path integral of magnetic field  along any closed path is zero. Hence from Ampere circuital law 

(where the given terms have usual meaning), no current can be present within a region having uniform and constant magnetic field.

In the circuit given below, both batteries are ideal. EMF E₁ of battery 1 has a fixed value, but emf E₂ of battery 2 can be varied between 1.0 V and 10.0 V. The graph gives the currents through the two batteries as a function of E₂, but are not marked as which plot corresponds to which battery. But for both plots, current is assumed to be negative when the direction of the current through the battery is opposite the direction of that battery's emf. (Direction of emf is from negative to positive)

The value of emf E1 is :

In the circuit given below, both batteries are ideal. EMF E₁ of battery 1 has a fixed value, but emf E₂ of battery 2 can be varied between 1.0 V and 10.0 V. The graph gives the currents through the two batteries as a function of E₂, but are not marked as which plot corresponds to which battery. But for both plots, current is assumed to be negative when the direction of the current through the battery is opposite the direction of that battery's emf. (Direction of emf is from negative to positive)

The resistance R1 has value :

In the circuit given below, both batteries are ideal. EMF E₁ of battery 1 has a fixed value, but emf E₂ of battery 2 can be varied between 1.0 V and 10.0 V. The graph gives the currents through the two batteries as a function of E₂, but are not marked as which plot corresponds to which battery. But for both plots, current is assumed to be negative when the direction of the current through the battery is opposite the direction of that battery's emf. (Direction of emf is from negative to positive)

The resistance R2 is equal to :

Curves in the graph shown give, as functions of radial distance r (from the axis), the magnitude B of the magnetic field (due to individual wire) inside and outside four long wires a, b, c and d, carrying currents that are uniformly distributed across the cross sections of the wires. Overlapping portions of the plots are indicated by double labels. All curves start from the origin.

Which wire has the greatest radius ?