JEE Main 2022 · 28 June · morning · Single correct · +4 / −1
Given below are two statements :
Statement I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.
Statement II : An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero.
Choose the correct answer from the options given below :
- (a) Both Statement I and Statement II are true.
- (b) Both Statement I and Statement II are false.
- (c) Statement I is true but Statement II is false.
- (d) Statement I is false but Statement II is true.
Answer and solution
Answer (a) Both Statement I and Statement II are true.
Solution
Physics sir · 4 steps
Fields add as vectors, and a non-uniform field pulls the two ends of a dipole unequally.
- Superposition. Once the point charge is placed, the field at any nearby point is the vector sum of the original field and the charge's own field. Where the two point the same way, the total is larger than before.
E⃗ₙₑₜ = E⃗ₑₓₜₑᵣₙₐₗ + 1/4πε₀q/r² r
- Statement I. A positive charge's field points away from it. At a point on the side where this outward field lines up with E⃗ₑₓₜₑᵣₙₐₗ, the net field grows. So the field may increase, and Statement I is true.
- Statement II. The +q end feels qE⃗₁ and the -q end feels -qE⃗₂. In a non-uniform field E⃗₁ ≠ E⃗₂, so the two forces do not cancel and the net force q(E⃗₁ - E⃗₂) is not zero. Statement II is true.
- So. Both statements are true, which is option (a).
The idea to keep. A dipole feels zero net force only in a uniform field. In a non-uniform field it feels a net force, and it may feel a torque as well. And always add fields as vectors before judging if one grows or shrinks.
Answer from the NTA final answer key. Solution by PrepWiser.