BITSAT 2024 Shift 1 Paper

The electric field E at point (30,30,0) due to a charge of 0.008µC placed at the origin can be calculated using the formula:
E=‌

Kq

r3

⋅r
Step 1: Calculate the distance r :
r=√(x2−x1)2+(y2−y1)2+(z2−z1)2
Substitute the given coordinates:
r=√302+302+02=30√2‌cm=30√2×10−2m
Step 2: Convert charge q to Coulombs:
q=8×10−3µC=8×10−3×10−6C
Step 3: The position vector r is:
r=(30

∧

i

+30

∧

j

)×10−2m
Step 4: Substitute into the electric field formula:
E=‌

9×109×8×10−3×10−6

(30√2×10−2)3

×(30

∧

i

+30

∧

j

)×10−2
Calculation:
E=‌

9×8×109×10−11

27×2√2×10−6×103

×30(

∧

i

+

∧

j

)
Simplify the expression:
‌E=‌

9×8×102×3

27×2√2

(

∧

i

+

∧

j

)
‌E=200√2(

∧

i

+

∧

j

)NC−1
Thus, the electric field at the given point is 200√2(

∧

i

+

∧

j

)NC−1.