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(C) The electric field $E_1$ at a distance $r$ from an infinitely long straight wire with linear charge density $\lambda$ is given by the formula: $E_

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$E_1 = E_2$

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(C) The electric field $E_1$ at a distance $r$ from an infinitely long straight wire with linear charge density $\lambda$ is given by the formula: $E_1 = \frac{\lambda}{2 \pi \epsilon_0 r} = \frac{2 k \lambda}{r}$,where $k = \frac{1}{4 \pi \epsilon_0}$.The electric field $E_2$ at the centre of a semicircular arc of radius $r$ with linear charge density $\lambda$ is calculated by integrating the field components: $E_2 = \frac{2 k \lambda}{r}$.Comparing the two expressions,we find that $E_1 = \frac{2 k \lambda}{r}$ and $E_2 = \frac{2 k \lambda}{r}$.Therefore,$E_1 = E_2$.

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