Physics: CUET Mock Test - 1 - JEE MCQ

The zone near a charge where its attraction or repulsion force works, is known as the electric field of that charge. Theoretically, it is up to infinite but practically it has limitations. If a unit positive charge is kept in that field, it will undergo some force which is known as electric field intensity at that point.

Though water and ammonia are covalent molecules, they have a net dipole moment due to their distorted structure than the ideal one. Hydrochloric acid has a linear molecular structure but its net dipole moment is towards the Hydrogen atom. But methane has a symmetrical tetrahedral structure and its net dipole moment is zero hence it doesn’t behave as a permanent dipole. Methane solvents are therefore non-polar solvents.

Force on a unit point charge kept at a distance r from the charge = q/r². Therefore, work done to bring that point charge through a small distance dr =(q/(r²)) * (-dr). Therefore, the potential of that point is =

When the resistors are connected in series, and current is passed through them, the current passing through each of the resistor is the same. This is because, the resistors are connected end to the end and, therefore, there is only one path for the current to flow through.

According to Kirchhoff’s first law, the current flowing towards the junction is equal to the current leaving the junction. Mathematically, this law can be expressed as ∑ⁿ_{K – 1} I_K = 0 (where n is the number of branches carrying current towards or away from the junction).

If a unit positive charge is kept near a negative charge, the unit positive charge will be attracted towards the negative charge. That means the electric field is towards the negative charge. But in case of positive charge, the field is directed away from the charge.

The dipole moment is defined as the product of a charge and distance. The dimension of charge (current*time) is [I T] and the dimension of distance is [L]. Therefore the dimension of dipole moment is [L T I]. Its unit in the CGS and the SI system are esu*cm and C*m respectively.

In the SI system, electric potential due to a point charge at a distance r is Substituting the values, we get potential=  Though in practice, this huge value of electric potential is not present.

When three resistors are connected in series, then the equivalent resistance of this combination is R_s = R₁ + R₂ + R₃. So, if 3 resistors having resistances 10, 15, and 20 ohms, are connected in series, then equivalent resistance of this combination is R_s = 10 + 15 + 20 = 45 ohms.

The equation → ∑e = ∑IR is applicable to Kirchhoff’s second law. This law is also known as Kirchhoff’s loop rule. This expression tells us that in a closed loop, the algebraic sum of the emfs is equal to the algebraic sum of the products of the resistance and currents flowing through them.

According to Gauss’s law, if there is no charge inside a closed surface, the field inside the closed surface will always be zero. We know the charge is distributed on the outer surface of a conducting hollow sphere because the charges want to maintain maximum distance among them due to repulsion. So there is no charge inside the sphere and hence no electric field.

If the distance of a point charge, kept on the axis of a dipole, is sufficiently large than the separation between the charges of a dipole, then it can be shown that electric field E at a distance r from the dipole varies as E α 1/(r³). Now if the distance becomes 2r, electric field intensity will decrease by a factor of 2³ = 8 times. Therefore the force F will now become F/8.

Work done = potential*charge by definition. We know that the potential of a point is the amount of work done to bring a unit charge from infinity to a certain point. Therefore, work done W = q * V = 4 * 10^-3 * 200J = 0.8J. The work done is positive in this case.

Domestic appliances in a house are connected in parallel combinations, and not in series combinations. This arrangement is done so that each of the appliances can switched on and off independently, which is essential in a house’s wiring.

According to sign convention while traversing a closed loop (in clockwise or anti-clockwise direction), if positive pole of the cell is encountered first then its emf is negative or else, it will be positive.

If the total charge of the sphere is q then the electric field at a distance of r is equal to  Therefore the electric field is proportional is (1/(r²)) (if r > radius of the sphere). But if r < radius of the sphere the electric field will be zero i.e. electric field inside a hollow sphere is always zero.

If the dipole moment of a dipole is p, then electric field intensity at a distance r from the dipole on its axis will be (2p/(r³)). But electric field intensity at a distance r from the dipole on its perpendicular bisector is (P/(r³)). Both the formulas are derived by assuming r >> length of the dipole. Thus E1= 2P/r³ and E2 = P/r³ and hence E1 = 2 E2.

Electric potential is a scalar quantity and its value is solely dependent on the charge near it and the distance from that charge. In this case, the point is equidistant from the two point charges and the point charges have the same value but opposite nature. Therefore equal but opposite potentials are generated due to the charges and hence the net potential at midpoint becomes zero.

The magnitude of the force acting on each of the charges will be the same and they will differ from each other by 120 degrees. Therefore their resultant force will always be zero.

Coulomb force is a strong force. It can be shown that the Coulomb force between two electrons is 1043 times than gravitational force. All the other options are basic properties of Coulomb’s Law.

If both the charges are of the same polarity (maybe of unequal magnitude), there must be a point in between them where the electric field intensities of the charges are of equal magnitude and in opposite direction. Hence they balance each other and the net field intensity must be zero. But if the charges are of opposite polarities their field intensities aid each other and net field intensity can never be zero.

Dipole is defined as two equal but opposite charges, kept at a small distance and having a dipole moment. The dipole moment is simply the product of the electric charge and length of the dipole. The dielectric constant of the medium doesn’t affect the dipole moment i.e. dipole moment of an electric dipole will be the same in water as well as in the air.

Distance of center from each corner point of the square is =  Therefore field intensity at the center due to a single charge is =  dyne/esu. But the fields due to the four charges are equal and are at perpendicular to each other. So the fields balance each other and the net electric field at the center will be equal to zero.

In parallel combination, the resistors are connected together at one end, and are also all connected together at the other end. So, the potential difference across the resistors will not change and thus, remains the same.

According to the diagram, Tsin⁡θ = Eq; Tcos⁡θ = mg. Where T is the tension in the thread, m is the mass of the ball, E is the electric field and q is the charge of the ball. Dividing these two, we get tanθ = Eq/mg. Now substituting the value of E=2*10⁴V/m, m=80mg, q=2*10^-8C, g=9.8m/s², we get tanθ = 25/49. Therefore θ=27 degree.

Dipole is the combination of two equal but opposite charges, kept at a certain distance. If it is placed in a uniform electric field, both the charges will suffer the same but opposite forces on them. As a result, the net force on the dipole becomes zero, but due to equal and opposite forces acting on two different points, there is a net torque acting on the dipole.

We know that electric field intensity at r distance from a point charge q is defined as q/r² in the CGS system. Here q=100 esu, r=10cm. Substituting the value we get E=1dyne/esu. We must remember that factor 1/4πε  is considered only in the SI system and its value is 9*10⁹, but in the CGS system, we simply take the value of this constant as unity.

We know that electric potential does not depend on the path, i.e. it is a state function. Therefore if we rotate a charge around another in a complete circular path, the potential energy of its initial and final points is the same. Therefore, there is no change of potential energy of the charge and hence net work done on the charge is zero.

Magnetic permeability = Magnetic flux density × [Magnetic field strength]^-1.
μ = [M L⁰ T^-2 A^-1] × [M⁰ L^-1 T⁰ A¹]^-1
μ = [M L T^-2 A^-2].

When θ = 0^o → τ = 0.
The torque is minimum when the plane of the loop is perpendicular to the magnetic field, so the angle θ should be 0^o.