A uniform field B=kt exists in a circular region. Points P and Q lie on the same circle of radius r

Question

A uniform field B=kt exists in a circular region. Points P and Q lie on the same circle of radius r<R and subtend angle θ. Determine the magnitude of ∫E·dℓ from P to Q along the circular arc.

G1 Physics · Accepted Answer

E=kr/2 and is tangential. The arc length is rθ, giving |∫E·dℓ|=kr²θ/2. Because this induced field is non-conservative, one should not interpret this as a path-independent electrostatic potential difference.