Practice Questions

Q12.A parallel plate capacitor is formed by two plates each of area 30π cm2 separated by 1 mm. A material of dielectric strength 3. 6 × 107 V m−1 is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is 7 × 10−6 C, the value of dielectric constant of the material is : [Use 1 = 9 × 109 N m2 C−2 ] 4πεo (1) 1. 66 (2) 1. 75 (3) 2. 25 (4) 2. 33

Q12.If the electric potential at any point (x, y, z) m in space is given by V = 3x2 volt. The electric field at the point (1, 0, 3) m will be : (1) 3 Vm−1 , directed along positive x-axis. (2) 3 Vm−1 , directed along negative x-axis. (3) 6 Vm−1 , directed along negative x-axis. (4) 6 Vm−1 , directed along positive x-axis.

Q12.A triangular shaped wire carrying 10 A current is placed in a uniform magnetic field of 0. 5 T, as shown in figure. The magnetic force on segment CD is (Given BC = CD = BD = 5 cm). (1) 0. 126 N (2) 0. 312 N (3) 0. 216 N (4) 0. 245 N

Q12.The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1. 2 × 10−5 . What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid? JEE Main 2022 (28 Jun Shift 2) JEE Main Previous Year Paper (1) 1. 2 × 10−5 (2) 1. 2 × 10−3 (3) 1. 8 × 10−3 (4) 2. 4 × 10−5

Q12.Find the equivalent resistance between point A and B (1) 65 Ω (2) 20 Ω (3) 5 Ω (4) 2 Ω

Q12.A long cylindrical volume contains a uniformly distributed charge of density ρ. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is : (1) ρqR2 (2) ρqR2 4εo 2εo (3) qρ (4) 4ε0R2 4ε0R2 qρ

Q12.A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 × 105 N C−1 . If the charge on the particle is 40 μC and the initial velocity is 200 m s−1 , how much distance it will travel before coming to the rest momentarily (1) 0. 5 m (2) 1 m (3) 5 m (4) 10 m

Q12.A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points A and B will be (1) 50V (2) 75V (3) 150V (4) 275V

Q12.A charge particle is moving in a uniform magnetic field (2ˆi 3ˆj) m s−2 , then the value of α will be (αˆi −4ˆj) (1) 3 (2) 6 (3) 12 (4) 2

Q13.Two parallel, long wires are kept 0. 20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is 2 × 10−6 N , then the value of x is approximately (1) 1 (2) 2. 4 (3) 1. 4 (4) 2

Q13.A small square loop of wire of side 𝑙 is placed inside a large square loop of wire 𝐿𝐿≫𝑙. Both loops are coplanar and their centres coincide at point 𝑂 as shown in figure. The mutual inductance of the system is (1) 2√2𝜇0𝐿2 (2) 𝜇0𝑙2 𝜋𝑙 2√2𝜋𝐿 (3) 𝜇0𝐿2 (4) 2√2𝜇0𝑙2 2√2𝜋𝑙 𝜋𝐿

Q13.A bar magnet having a magnetic moment of 2. 0 × 105 J T−1 , is placed along the direction of uniform magnetic field of magnitude B = 14 × 10−5 T. The work done in rotating the magnet slowly through 60° from the direction of field is (1) 14 J (2) 8 J (3) 4 J (4) 1. 4 J ∘

Q13.A capacitor is discharging through a resistor R. Consider in time t1 , the energy stored in the capacitor reduces to half of its initial value and in time t2 , the charge stored reduces to one eighth of its initial value. The ratio t2t1 will be (1) 1 (2) 1 2 3 (3) 1 (4) 1 4 6

Q13.Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3 : 2 then the ratio of their magnetic moments will be (1) 2 : 1 (2) 8 : 3 (3) 1 : 3 (4) 27 : 16

Q13. BX and BY are the magnetic field at the centre of two coils of two coils X and Y respectively, each carrying equal current. If coil X has 200 turns and 20 cm radius and coil Y has 400 turns and 20 cm radius, the ratio of BX and BY is JEE Main 2022 (26 Jul Shift 1) JEE Main Previous Year Paper (1) 1 : 1 (2) 1 : 2 (3) 2 : 1 (4) 4 : 1

Q13.A parallel plate capacitor filled with a medium of dielectric constant 10 , is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15 . Then the energy of capacitor will (1) increase by 50% (2) decrease by 15% (3) increase by 25% (4) increase by 33%

Q13.A 72 Ω galvanometer is shunted by a resistance of 8 Ω. The percentage of the total current which passes through the galvanometer is (1) 0. 1% (2) 10% (3) 25% (4) 0. 25%

Q13.A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is (1) 4 : 1 (2) 2 : 1 (3) 1 : 2 (4) 1 : 4

Q13.A sinusoidal voltage 𝑉𝑡= 210sin3000𝑡 volt is applied to a series LCR circuit in which 𝐿= 10 mH, 𝐶= 25 μF and 𝑅= 100Ω. The phase difference 𝛷 between the applied voltage and resultant current will be (1) tan-10 . 17 (2) tan-19 . 46 (3) tan-10 . 30 (4) tan-113 . 33

Q13.If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be JEE Main 2022 (27 Jun Shift 2) JEE Main Previous Year Paper (1) q (2) q ε0 2ε0 (3) q (4) q 4ε0 2πε0

Q13.A 1 m long wire is broken into two unequal parts 𝑋 and 𝑌. The 𝑋 part of the wire is stretched into another wire 𝑊. Length of 𝑊 is twice the length of 𝑋 and the resistance of 𝑊 is twice that of 𝑌. Find the ratio of length JEE Main 2022 (29 Jul Shift 2) JEE Main Previous Year Paper of 𝑋 and𝑌. (1) 1: 4 (2) 1: 2 (3) 4: 1 (4) 2: 1

Q13.As shown in the figure, a metallic rod of linear density 0 . 45 kg m-1 is lying horizontally on a smooth incline plane which makes an angle of 45° with the horizontal. The minimum current flowing in the rod required to keep it stationary, when 0 . 15 T magnetic field is acting on it in the vertical upward direction, will be (Use 𝑔= 10 m s-2) (1) 30 A (2) 15 A (3) 10 A (4) 3 A JEE Main 2022 (28 Jul Shift 1) JEE Main Previous Year Paper

Q13.An alternating emf E = 440 sin 100πt is applied to a circuit containing an inductance of √2π H . If an a.c. ammeter is connected in the circuit, its reading will be : (1) 4. 4 A (2) 1. 55 A (3) 2. 2 A (4) 3. 11 A

Q13.The magnetic field at the center of current carrying circular loop is B1 . The magnetic field at a distance of √3 times radius of the given circular loop from the center on its axis is B2 . The value of B1B2 will be (1) 9 : 4 (2) 12 : √5 (3) 8 : 1 (4) 5 : √3

Q13.The electric field in an electromagnetic wave is given by 𝐸= 56 . 5sin𝜔 𝑐NC-1. Find the intensity of the wave if it is propagating along 𝑥-axis in the free space. (Given 𝜖0 = 8 . 85 × 10-12C2 N-1 m-2) (1) 5 . 65Wm-2 (2) 1 . 9 × 10-7Wm-2 (3) 4 . 24 Wm-2 (4) 56 . 5Wm-2