In a region, the potential is V(x,y,z) = 6x − 8xy − 8y + 6yz, with V in volts and x,y,z in metres. The electric force experienced by a charge of 2 coulomb located at point (1,1,1) is:
Physics · Electrostatic · Electric Potential & Potential Energy
AIPMT 2014 NEET Previous Year

Question

In a region, the potential is V(x,y,z) = 6x − 8xy − 8y + 6yz, with V in volts and x,y,z in metres. The electric force experienced by a charge of 2 coulomb located at point (1,1,1) is:

G1 Physics · Accepted Answer

Step 1: Field components E = −∇V: Eₓ = −6 + 8y, Eᵧ = 8x + 8 − 6z, E𝓏 = −6y. Step 2: At (1,1,1), E⃗ = 2î +10ĵ −6k̂. Step 3: |E⃗| = √(4+100+36) = √140 = 2√35 N/C. Step 4: |F| = q|E⃗| = 2 × 2√35 = 4√35 N.