A long straight wire of radius $$a$$ carries a steady current $$i.$$ The current is uniformly distributed across its cross section. The ratio of the magnetic field at $$a/2$$ and $$2a$$ is

A current $$I$$ flows along the length of an infinitely long, straight, thin walled pipe. Then

A charged particle with charge $$q$$ enters a region of constant, uniform and mutually orthogonal fields $$\overrightarrow E $$ and $$\overrightarrow B $$ with a velocity $$\overrightarrow v $$ perpendicular to both $$\overrightarrow E $$ and $$\overrightarrow B, $$ and comes out without any change in magnitude or direction of $$\overrightarrow v $$. Then

The resistance of a wire is $$5$$ ohm at $${50^ \circ }C$$ and $$6$$ ohm at $${100^ \circ }C.$$ The resistance of the wire at $${0^ \circ }C$$ will be