The electric field due to an infinitely long thin straight wire with uniform linear charge density of 2.5×10−7cm−1 at a radial distance of x from the wire is 7.5×104NC−1. Then, x=
Step 1: Formula for electric field around a long wire The electric field ( E ) at a distance x from a very long straight wire with charge per unit length ( λ ) is given by: E=‌
2Kλ
x
Here, K is Coulomb's constant (K=9×109Nm2C−2). Step 2: Substitute the given values We are given: ‌E=7.5×104N∕C ‌λ=2.5×10−7C∕m ‌K=9×109Nm2C−2 So, 7.5×104=‌
2×9×109×2.5×10−7
x
Step 3: Solve for x Multiply the numbers on the right side first: ‌2×9=18 ‌18×2.5=45 So, top becomes: 45×109×10−7=45×102=4500 So: 7.5×104=‌
4500
x
Step 4: Rearrange to find x Multiply both sides by x and divide both sides by 7.5×104:x=‌