If uniform electric field ` vec E = E_ 0 hati + 2 E _ 0 hatj `, where ` E _ 0 ` is a constant exists in a region of space and at (0,0) the electric potential V is zero, then the potential at ` ( x _ 0 , 2x _ 0 ) ` will be -

Options

A. zero
B. ` - 5E _ 0 x _ 0 `
C. ` - 3 E _ 0 x _ 0 `
D. `-sqrt5 E _ 0 x _ 0 `

Answer

B

Explanation

A in (0, 0) and B is ` ( x _ 0, 2 x _0) `
` V _ B- V_ A= - int _ A^ B vec E .d vecs `
`rArr V_ B = - int _ A^B vecE.decs `
` vecE = E_0 hati + 2 E _ 0 hatj `
` d vecs = dx hati + dy hatj `
` int _ ("(0,0)")^("(" x _ 0, 2 x _ 0")") vecE. d vecs = int _ (0, 0)^ ( x _ 0, 2 x _ 0 ) ( E _0 hati + 2 E _ 0 hatj ) * ( dx hati + dy hatj ) `
`rArr V _ B = - 5 E _ 0 x _ 0 `